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An inexact Picard iteration method for absolute value equation

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Shu-Xin Miao, Xiang-Tuan Xiong, Jin Wen

Numerical Analysis · Submitted 30 Sep 2015

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

The authors' main claim Some numerical experiments are given to demonstrate the effectiveness of the new method.

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arXiv ID1509.09102 (version 1)
Pith IDF7OXS4JS, Pith's permanent record of this paper and its review
CitationJin Wen, Shu-Xin Miao, Xiang-Tuan Xiong. "An inexact Picard iteration method for absolute value equation." arXiv:1509.09102 (2015). https://pith.science/paper/F7OXS4JS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,566 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.49 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Recently, a class of inexact Picard iteration method for solving the absolute value equation: $Ax-|x~|=b$ have been proposed in [Optim Lett 8:2191-2202,2014]. To further improve the performance of Picard iteration method, a new inexact Picard iteration method is proposed to solve the absolute value equation. The sufficient conditions for the convergence of the proposed method for the absolute value equation is given. Some numerical experiments are given to demonstrate the effectiveness of the new method.

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 Recently, a class of inexact Picard iteration method for solving the absolute value equation: $Ax-|x~|=b$ have been proposed in [Optim Lett 8:2191-2202,2014]. background 1.00 0.04 0.03 asserted 1.00
s1 To further improve the performance of Picard iteration method, a new inexact Picard iteration method is proposed to solve the absolute value equation. contribution 0.99 0.92 0.32 asserted 1.00
s2 The sufficient conditions for the convergence of the proposed method for the absolute value equation is given. contribution 0.72 0.91 0.36 asserted 1.00
s3 Some numerical experiments are given to demonstrate the effectiveness of the new method. result 0.36 0.93 0.15 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.58.

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  • figures and tables
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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

Recently, a class of inexact Picard iteration method for solving the absolute value equation: $Ax-|x~|=b$ have been proposed in [Optim Lett 8:2191-2202,2014]. To further improve the performance of Picard iteration method, a new inexact Picard iteration method is proposed to solve the absolute value equation. The sufficient conditions for the convergence of the proposed method for the absolute value equation is given. Some numerical experiments are given to demonstrate the effectiveness of the new method.

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