Pith. sign in

Paper Citation Record · LEDGER

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients

As of 7 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 0 inbound Pith citation observations for arXiv:2507.23408.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.23408 v1

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:57:05.473739Z

measured 62 of 62 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

62 of 62 outbound references displayed

  • verified exact3
  • verified fuzzy15
  • unresolved44
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cd7ccb48-8591-4845-b910-d0e882766fbc · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:06.031388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.302924Z digest=sha256:87f954db0e19b1203a9f6ef7ec1a685cc8c8d9612543ca11212bf84c054240ce

Observation c839ef6d-fe2c-439f-b6a4-ac2cda66063e · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:06.023037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.306640Z digest=sha256:108cc6d3e55f30ace5d217ae2cb7e3b74c3fc3fd86f127ac6c6fcc63b1fb5ed4

Observation 9f4d5e72-efef-435c-b29c-c3ce4298209b · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:06.014875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.309667Z digest=sha256:524a0ee27609742d539851ea47586a5d3dce13a1ef2d587bad0637b172336920

Observation dcc289e4-dbb6-4627-a8a6-856ff585f508 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:06.006181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.312664Z digest=sha256:c74d45c61cebb7a5b1bcaa373272fa44dd554e2ca8718c190df800a147dfd4f7

Observation daa391cc-e003-446a-b846-1d1bbfe2674b · outbound

This paper cites Raberto, E.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Raberto, E

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.997299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.315637Z digest=sha256:8066126e57bc68072760ae1843353dc1b55d60325f048944f1f846b9b9ab8322

Observation d212a073-10de-4d09-afd2-d44707c0d679 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.988766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.318341Z digest=sha256:feda8f67abc973baf219fc025036504228d521df4f98e412ed80f9069b4aed32

Observation 5e1b2ad2-e023-4008-ae63-1ff770f46dd7 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.979861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.321298Z digest=sha256:7ed0e29cb9e1d54a17fc5d58e61903c84e46b2c5d769c4bf4175ca8fb3c7cf00

Observation 55206b1c-71de-4921-a8fe-9e305a5de89b · outbound

This paper cites Sousa, C.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Sousa, C

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.971714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.323931Z digest=sha256:34cf92ef1bb57fa9d199aaeba77a9197658c0fe8ab0c92eb88d724fbca8247ed

Observation aca4d942-70a5-4565-92b8-884f0906ae38 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.962945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.326467Z digest=sha256:dd798e68fd44d113da722066a8ef0e75fa92dc3dbd6ea32fc04cc71a4a1e9a77

Observation 2288a9f3-7d71-4890-a9a7-95fe1e788f0a · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.954563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.329125Z digest=sha256:65325d01b40a3dc11b89da27f2852e84aef212046aea28d49560389b0fa135f7

Observation 34d2955e-3519-461a-a901-bc6eeffb6d87 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.946369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.331570Z digest=sha256:6474f58637716fbec6005aeb9c411985e442e5e95192444bea65a912ab1f2f77

Observation 9f03d35c-c0ae-42d4-a661-050aec2f98a3 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.938153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.334336Z digest=sha256:ef7c8698ce741ce09b6f0d6c02d61cb30e6972655bb8b49e196f0a2118542d6f

Observation 7c4544ab-89cb-4c6b-8a46-d5a4afb0b643 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.929731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.336806Z digest=sha256:f5b74e83634bf6b390ca77bd8ec8d993922ef75bdf98d0f8c3d5e2206825412b

Observation 0de98905-29ad-4361-9308-6a0fcada04c9 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.921409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.339410Z digest=sha256:4a76de9a50f7790faa121d6741978548034a407074f3f1eee2f2ad861a8cf4ce

Observation fc798467-2063-403a-83d8-09ca627b71f5 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.913028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.341973Z digest=sha256:ee07ca30e8aba7fb4f80eac4f438bce76bab8da151c2241b3a67309441e68b61

Observation d6ae4896-0e7b-443d-9b56-9fc8faeac2af · outbound

This paper cites Donatelli, M.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Donatelli, M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.904628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.344576Z digest=sha256:680f2a68827a42ad47693b1cdc3e2282c9a9308d8bebe84839cc530fb7294473

Observation 5180f773-b1cb-4473-9466-a99e05fe5458 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.896190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.347193Z digest=sha256:61752073f266af986f1d4e39ea3f93dd6ddcbc758278f68fd47b612cb8a8bd8d

Observation dbbe4217-dc22-48ba-a250-652597c6adcc · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.887609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.349770Z digest=sha256:3670fde8477ff3a8f997f78a89360ae3234bf8f602d6cd6a479c17137c5f2ae8

Observation 002be7e9-27e7-4ea6-a109-f06d852749f6 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.879488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.352460Z digest=sha256:dff9280e6f2ca0b046554595ff644093bdaf039946b4bda154567b6c5166db5e

Observation 528aaa79-0fe9-4289-aa83-97991dedd986 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.871034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.355110Z digest=sha256:bd5a24dcaf0e95c8a9de6e2f7d12fb8bd9b976d0260156465fd54785e5716932

Observation a8a74831-cc00-4f02-8440-1f1160e596fa · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.862308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.357726Z digest=sha256:b86709907bbcfc63c82c5703889f74045d2e8d63a4af239936cb4481a19326bd

Observation 39a0fee8-b9b4-4778-89ec-a0b529a24772 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.853873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.360439Z digest=sha256:bdd84d904f72ee150a67e45dea7ce6f24b0f31cdd2a3907bedcfd711aa05546d

Observation 37949025-f47c-4ef6-ba88-8cbf85db9c6b · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.844728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.362940Z digest=sha256:d65a0b78d4eb60b819e6060652b7edb0825a1c0e61c8ca2cffb7845d9d92fae5

Observation e81b0b02-a20a-4865-9883-9a8adfb47183 · outbound

This paper cites Moghaderi, M.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Moghaderi, M

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.836086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.365649Z digest=sha256:d45a8def386dc306f742b1441910a9e054015da0d8efe833434244436d9dd699

Observation 7791d80e-9559-4acb-8830-fe3292a398c6 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.827204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.368217Z digest=sha256:733fd9bdf5bb3a2ba329a2481498877cf6c1a589d009850e45b4f4aa5d36c63b

Observation 7bf7778d-1403-48c1-8893-d1870688b879 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.818259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.370867Z digest=sha256:236b608bdecc6e3e1f5d44989a5e70e0905f6aced60a471cedfe1695ba04ee50

Observation 208ed5e1-faa4-455e-97ac-4d18ee60ad0e · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.809811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.373477Z digest=sha256:d85b91bdf9948b33ea38f843438f4128d74359ae3e38250abb36cb207ca05247

Observation 376a635f-a5b8-4ab8-afdb-e2084a273741 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.801414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.376508Z digest=sha256:62f52130ce8f0dcd1d58655a589842a967cfa790c7b9a4b5fcfa3cf7caf7cb1d

Observation f4f1fe9c-abc9-442d-814a-ba5c05636ffd · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.792883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.379286Z digest=sha256:d70393531a0007b55c605696425571874f6f2997c8519857e8cd1945be659a8c

Observation 7e11d780-93d6-41df-a539-00ba2d45faca · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.784651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.381879Z digest=sha256:5cf68334b1d9f1eeecf74f22c2065cfe45278772778c41f4a34d9b44ef76b036

Observation c0fa1295-8454-4db1-aa16-d0db7078c095 · outbound

This paper cites Donatelli, M.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Donatelli, M

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.776082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.384639Z digest=sha256:8f27aea20239cd95a82cacecc661a47f852fc23412a74d4390a009b14e8d2f38

Observation 054008a6-d0be-46e0-862f-4be1188300c8 · outbound

This paper cites Aceto, M.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Aceto, M

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.767683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.387372Z digest=sha256:45d35e1da8b38934e52def8a4ad47f1709cc1a231120d878303488c98fd42a60

Observation 4b714c8c-fc7b-47ac-9002-a333879535a7 · outbound

This paper cites Huang, X.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Huang, X

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.759210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.389998Z digest=sha256:2c14c749e7cda2177aee37c35014f5aaa33259c655d2faf71f8822c7ee704deb

Observation e53989f8-d494-42e4-8bb5-e4f93650302a · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.748809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.392763Z digest=sha256:599c3f9afef9eb3442e3428c8a8eee1a452cf3fb85511b2e99ceb66933d906ca

Observation be59643b-c884-493b-a32f-54f372fb43d4 · outbound

This paper cites Symbol-based multilevel block $\tau$ preconditioners for multilevel block Toeplitz systems: GLT-based analysis and applications.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Symbol-based multilevel block $\tau$ preconditioners for multilevel block Toeplitz systems: GLT-based analysis and applications

Reference 35

Resolution
verified exact
local_arxiv, observed 2026-08-06T10:57:05.530096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.395726Z digest=sha256:fa63975e6a2e79a81974499ef24a5e4f7bbffe2798a8446817d644de3035f77f

Observation b2037faa-28f7-42fc-8b78-94066473b700 · outbound

This paper cites Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations

Reference 36

Resolution
verified exact
local_arxiv, observed 2026-08-06T10:57:05.518642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.399200Z digest=sha256:b1eaaff77e6431ca47af6b491ad51e91a59b3b63b23c7819786e3cede1344c49

Observation 26debb98-b440-4359-824f-dfe97e44767f · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.739224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.402227Z digest=sha256:0753bd1df03eea68a907f5bb701cddb429d90a86986b7d2655e5bb5b40d15d32

Observation 4eedaa6f-b8cf-4c67-bf1a-e6fe8fa3af2c · outbound

This paper cites Huang, P.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Huang, P

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.729833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.404939Z digest=sha256:34e46c0e45d88ac5fc078a1d9be0432a6888cbafd742f8b6c0a4b9a9da81e4c8

Observation f5cb7750-5a8c-4aff-8749-bdb08d9f1cc3 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.720026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.407808Z digest=sha256:642589fcf5d9ff22e37455a4d329e56afa58fa68c278fc8bd9a8d507dda97fe4

Observation 2bf1ac7d-4d5e-46de-b534-1178120c44cf · outbound

This paper cites Zhang, X.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Zhang, X

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.711177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.410540Z digest=sha256:c137f9c5e2dbd3b6b073dea3f53e1e35593ffd2bdabf9111300ffd4f55cee6e5

Observation 76b0aa79-02e1-4591-baea-bf274860d73b · outbound

This paper cites On $\tau$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients On $\tau$-preconditioners for a quasi-compact difference scheme to Riesz fractional diffusion equations with variable coefficients

Reference 41

Resolution
verified exact
local_arxiv, observed 2026-08-06T10:57:05.505820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.413304Z digest=sha256:8ad7fb969362b5016e50a1c816ff47c8c9c3d9d285d35895b4a0cdcb71344ecb

Observation 52751bb5-91f3-4773-a83b-d920d77f5e32 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.702658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.416230Z digest=sha256:1b957a1beac275ef92265716f41fa70b19b0072d794d830ae1f846b49d7bdecc

Observation 667c936b-e294-473e-8bd1-1ef882f08bd9 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.694609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.418969Z digest=sha256:1d3adce5ca6d051aa4205ee8307fb982199d9a8a8ededc661e7d7ac21e8aa4cb

Observation 1a5bafce-abff-45fb-867b-4b328b4698f5 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.686534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.421766Z digest=sha256:ecb6b408ef6706157a36aaa45a192a39fc3df15d450d64d93976ddcf853effe0

Observation d02f0b4c-11b2-45f0-a382-5434d229fa2b · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.678596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.424555Z digest=sha256:80fa277e7e3264f6d977cd5235d549afce5095b54ce1d360859cc0d70400ac34

Observation 1af153f1-58c8-459b-aa55-4a36a35720d1 · outbound

This paper cites Serra, Superlinear PCG methods for symmetric Toeplitz systems, Math.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Serra, Superlinear PCG methods for symmetric Toeplitz systems, Math

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.670904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.427232Z digest=sha256:ebfd1734b81f58a6a2852e94a60ae6a58ee0c737e9e6c141d1f16d7d92501152

Observation ca462013-81df-4260-9e92-52d4955e6575 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.662889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.430035Z digest=sha256:700df9d42356345193091d3324c8b67b3c10965b44b7cfccd0a82b8fa86303e2

Observation 4ef290d0-e11e-4f5b-ba0c-e6370b9d149b · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.654254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.432795Z digest=sha256:880d343c6bfbe5dcd3ec69cd370a339951015ad8c4d382e6ea7e9aab6ff6d9a5

Observation aac0e3de-de2e-4f40-9061-f598744b3ba4 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.646540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.435556Z digest=sha256:dff3614464335152819ab1e586dce1a4df6a71977cde3c521cd975bf58d65762

Observation 7e4c6586-c343-4ea1-8226-6d19b0dc8f5f · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.637982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.438407Z digest=sha256:649c26eaf56755cf70d3ab2582cf60f85749788485c5629b2ba26c1ef36bcabb

Observation df409fa3-4ae3-4bf9-888d-cbf57fc67149 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.630165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.441172Z digest=sha256:4aefe5b2d383575e0fb97c668b5efc459e7a0194878af619a478da8f48723f3e

Observation 486a6cb2-38a7-4a61-9386-d965cee66656 · outbound

This paper cites Greenbaum, V.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Greenbaum, V

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.622242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.444309Z digest=sha256:768497200f0e40f7791e936dbf1fa792faff1df608d382d6689537b13cb8e1b9

Observation bf4542af-11fe-4e76-bf5d-f5c2503a7412 · outbound

This paper cites Greenbaum, Z.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Greenbaum, Z

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.614000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.447294Z digest=sha256:573687de41580e08411d95b541506977f50b1838b5dffb930d1db463e463326e

Observation 018fdb23-653b-482f-9f13-4ff95aa1b24d · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.604984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.450365Z digest=sha256:0ebb2e814cb92040fb026ed19e8742cec3dfb075f23fd4779aaa2a2fa95bbbff

Observation e8cd8ba2-8dbb-4e51-8c81-f78000dc8609 · outbound

This paper cites C ¸ elik, M.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients C ¸ elik, M

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.597147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.453196Z digest=sha256:e9a48e21e98a53bbe487ab5dfe36a30876e916e39c6cdc4eabcc949d91f3aa71

Observation a3cc64e5-8414-48e3-88d7-b489f6683757 · outbound

This paper cites Zhang, X.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Zhang, X

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.588870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.456041Z digest=sha256:bb9e7ef70ee9ee0dd3af5e906d3ddad544783277e2a74d4e8a631c6cc73d0f42

Observation 054f74fd-58ff-4ac0-8d4e-9e633b4a2c68 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.580906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.458806Z digest=sha256:8bccc06ac1f20e5dca7179c791312395bf440b14aee07989ab91f7ca3f5d40f0

Observation 7d2e620d-a37d-4c17-8a5e-c3c8bd42bc50 · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.572630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.461616Z digest=sha256:317c20b8b40dcefef3266cf3e2b6bd9ab0f2732d531a44e0d1cbd5a159fc27a3

Observation 2e5aaede-791d-4edb-a647-c592a37e805e · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.564541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.464419Z digest=sha256:61f8196cb158bd98d10a3b5d16028634fce33089684d3b07db2d38623abadb38

Observation ea0429df-1b5b-476e-aa0a-7e18f46e912b · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.556351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.467538Z digest=sha256:96b10e41285e864238c6aaaed27b59a7b014626babf2762acf2ca65ea9c15175

Observation 1df91f0b-e2fc-45be-a183-91a073e4a12f · outbound

This paper cites an unresolved cited work.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:57:05.547586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.471033Z digest=sha256:228e9abb47b6b95488330e5552d65180450f14270f0523f9dccd3188e9e15802

Observation fddfcd02-b0ae-426e-8ac5-ea6403f4387b · outbound

This paper cites Greenbaum, Iterative methods for solving linear systems, SIAM, 1997.

An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients Greenbaum, Iterative methods for solving linear systems, SIAM, 1997

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:57:05.538975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T10:57:05.473739Z digest=sha256:5024dfedfcdd7f31748d953b2a1032ebe73a4db599aeffcaae7c07da6b9b75b2

Pith citing papers

No inbound Pith citation observations are available.