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Robust iteration methods for complex systems with an indefinite matrix term

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Owe Axelsson, Maeddeh Pourbagher, Davod Khojasteh Salkuyeh

Numerical Analysis · Submitted 1 Oct 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim To handle this we propose different forms of matrix splitting methods, with or without any parameters involved.

how it is stated · asserted 0.98 read the record →

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arXiv ID2110.00537 (version 1)
Pith IDYOZQZUGV, Pith's permanent record of this paper and its review
CitationDavod Khojasteh Salkuyeh, Maeddeh Pourbagher, Owe Axelsson. "Robust iteration methods for complex systems with an indefinite matrix term." arXiv:2110.00537 (2021). https://pith.science/paper/YOZQZUGV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,234 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. background 1.00 0.05 0.03 asserted 1.00
s1 Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. background 1.00 0.10 0.06 asserted 0.99
s2 The appearances of an indefinite matrix term causes however some difficulties. background 0.68 0.08 0.02 asserted 1.00
s3 To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. contribution 0.74 0.90 0.13 asserted 0.98
s4 A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods. contribution 0.58 0.92 0.13 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.93.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with symmetric positive definite matrices can be solved readily by rewriting the complex matrix system in two-by-two block matrix form with real matrices which can be efficiently solved by iteration using the preconditioned square block (PRESB) preconditioning method and preferably accelerated by the Chebyshev method. The appearances of an indefinite matrix term causes however some difficulties. To handle this we propose different forms of matrix splitting methods, with or without any parameters involved. A matrix spectral analyses is presented followed by extensive numerical comparisons of various forms of the methods.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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