Pith Number

pith:G6RUC7LE

pith:2026:G6RUC7LE4TGG7WRRMUHR6HDVG7

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A mixed interpolation-regression method for function approximation on certain planar domains

Francisco Marcell\'an, Juan Antonio Villegas, Lidia Fern\'andez, Ruym\'an Cruz-Barroso

A mixed interpolation-regression operator is introduced for functions on ellipses, annuli, and polygons, yielding an upper bound and cubature formulas.

arxiv:2604.24748 v2 · 2026-04-27 · math.NA · cs.NA

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\pithnumber{G6RUC7LE4TGG7WRRMUHR6HDVG7}

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Record completeness

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. An upper bound for such an operator is obtained. Cubature formulas for weight functions defined in such domains are studied.

C2weakest assumption

The operator and bound hold for the specific domains (ellipse, annulus, polygon) and weight functions considered; the abstract does not state the precise function class or smoothness requirements needed for the bound to apply.

C3one line summary

A hybrid interpolation-regression operator is defined for numerical integration over ellipses, annuli, and polygons, with an operator norm bound and associated cubature formulas.

Receipt and verification

First computed	2026-06-11T01:10:36.742076Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

37a3417d64e4cc6fda31650f1f1c7537c851395af37f4170416efb8cc1e88ab4

Aliases

arxiv: 2604.24748 · arxiv_version: 2604.24748v2 · doi: 10.48550/arxiv.2604.24748 · pith_short_12: G6RUC7LE4TGG · pith_short_16: G6RUC7LE4TGG7WRR · pith_short_8: G6RUC7LE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/G6RUC7LE4TGG7WRRMUHR6HDVG7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 37a3417d64e4cc6fda31650f1f1c7537c851395af37f4170416efb8cc1e88ab4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "235001ff3eb460b3d896c0f86740a511e34783414acc34001249ecf977b2e1a4",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-27T17:51:04Z",
    "title_canon_sha256": "a87f96f3503c0ba8513f732308b5959a874f5ca46bbe2a2e664c868722b55acc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24748",
    "kind": "arxiv",
    "version": 2
  }
}