A generalization of the relaxation-based matrix splitting iterative method for solving the system of generalized absolute value equations Article Swipe

PDF

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2312.10891

By incorporating a new matrix splitting and the momentum acceleration into the relaxed-based matrix splitting (RMS) method \cite{soso2023}, a generalization of the RMS (GRMS) iterative method for solving the generalized absolute value equations (GAVEs) is proposed. On the one hand, unlike some existing methods, by using the Cauchy's convergence principle we give some sufficient conditions for the existence and uniqueness of the solution to GAVEs and prove that our method can converge to the unique solution of GAVEs. On the other hand, we obtain a few new and weaker convergence conditions for some existing methods. Moreover, we establish comparison theorems between GRMS method and some existing methods. Preliminary numerical experiments show that the proposed method is efficient.

Related Topics

Mathematics

Generalization

Mathematical Analysis

Concepts

Uniqueness Mathematics Generalization Convergence (economics) Matrix (chemical analysis) Relaxation (psychology) Initial value problem Applied mathematics Absolute convergence Cauchy distribution Iterative method Mathematical analysis Mathematical optimization Fourier series Economic growth Social psychology Materials science Economics Composite material Psychology

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2312.10891
PDF: https://arxiv.org/pdf/2312.10891
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4389983839

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4389983839

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2312.10891

Digital Object Identifier
Title: A generalization of the relaxation-based matrix splitting iterative method for solving the system of generalized absolute value equations

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-12-18

Full publication date if available
Authors: Xuehua Li, Cairong Chen

List of authors in order
Landing page: https://arxiv.org/abs/2312.10891

Publisher landing page
PDF URL: https://arxiv.org/pdf/2312.10891

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2312.10891

Direct OA link when available
Concepts: Uniqueness, Mathematics, Generalization, Convergence (economics), Matrix (chemical analysis), Relaxation (psychology), Initial value problem, Applied mathematics, Absolute convergence, Cauchy distribution, Iterative method, Mathematical analysis, Mathematical optimization, Fourier series, Economic growth, Social psychology, Materials science, Economics, Composite material, Psychology

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4389983839
doi	https://doi.org/10.48550/arxiv.2312.10891
ids.doi	https://doi.org/10.48550/arxiv.2312.10891
ids.openalex	https://openalex.org/W4389983839
fwci
type	preprint
title	A generalization of the relaxation-based matrix splitting iterative method for solving the system of generalized absolute value equations
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10792
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	0.9993000030517578
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1703
topics[0].subfield.display_name	Computational Theory and Mathematics
topics[0].display_name	Matrix Theory and Algorithms
topics[1].id	https://openalex.org/T10963
topics[1].field.id	https://openalex.org/fields/26
topics[1].field.display_name	Mathematics
topics[1].score	0.9793999791145325
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2612
topics[1].subfield.display_name	Numerical Analysis
topics[1].display_name	Advanced Optimization Algorithms Research
topics[2].id	https://openalex.org/T12661
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9781000018119812
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2612
topics[2].subfield.display_name	Numerical Analysis
topics[2].display_name	Iterative Methods for Nonlinear Equations
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C2777021972
concepts[0].level	2
concepts[0].score	0.7133362293243408
concepts[0].wikidata	https://www.wikidata.org/wiki/Q22976830
concepts[0].display_name	Uniqueness
concepts[1].id	https://openalex.org/C33923547
concepts[1].level	0
concepts[1].score	0.7039598226547241
concepts[1].wikidata	https://www.wikidata.org/wiki/Q395
concepts[1].display_name	Mathematics
concepts[2].id	https://openalex.org/C177148314
concepts[2].level	2
concepts[2].score	0.6706339716911316
concepts[2].wikidata	https://www.wikidata.org/wiki/Q170084
concepts[2].display_name	Generalization
concepts[3].id	https://openalex.org/C2777303404
concepts[3].level	2
concepts[3].score	0.6421574950218201
concepts[3].wikidata	https://www.wikidata.org/wiki/Q759757
concepts[3].display_name	Convergence (economics)
concepts[4].id	https://openalex.org/C106487976
concepts[4].level	2
concepts[4].score	0.6282780170440674
concepts[4].wikidata	https://www.wikidata.org/wiki/Q685816
concepts[4].display_name	Matrix (chemical analysis)
concepts[5].id	https://openalex.org/C2776029896
concepts[5].level	2
concepts[5].score	0.6239610910415649
concepts[5].wikidata	https://www.wikidata.org/wiki/Q3935810
concepts[5].display_name	Relaxation (psychology)
concepts[6].id	https://openalex.org/C26955809
concepts[6].level	2
concepts[6].score	0.593838632106781
concepts[6].wikidata	https://www.wikidata.org/wiki/Q10167591
concepts[6].display_name	Initial value problem
concepts[7].id	https://openalex.org/C28826006
concepts[7].level	1
concepts[7].score	0.5681359767913818
concepts[7].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[7].display_name	Applied mathematics
concepts[8].id	https://openalex.org/C84122041
concepts[8].level	3
concepts[8].score	0.5176551938056946
concepts[8].wikidata	https://www.wikidata.org/wiki/Q332465
concepts[8].display_name	Absolute convergence
concepts[9].id	https://openalex.org/C49344536
concepts[9].level	2
concepts[9].score	0.48459041118621826
concepts[9].wikidata	https://www.wikidata.org/wiki/Q726441
concepts[9].display_name	Cauchy distribution
concepts[10].id	https://openalex.org/C159694833
concepts[10].level	2
concepts[10].score	0.4809969365596771
concepts[10].wikidata	https://www.wikidata.org/wiki/Q2321565
concepts[10].display_name	Iterative method
concepts[11].id	https://openalex.org/C134306372
concepts[11].level	1
concepts[11].score	0.4531524181365967
concepts[11].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[11].display_name	Mathematical analysis
concepts[12].id	https://openalex.org/C126255220
concepts[12].level	1
concepts[12].score	0.20615047216415405
concepts[12].wikidata	https://www.wikidata.org/wiki/Q141495
concepts[12].display_name	Mathematical optimization
concepts[13].id	https://openalex.org/C207864730
concepts[13].level	2
concepts[13].score	0.06820836663246155
concepts[13].wikidata	https://www.wikidata.org/wiki/Q179467
concepts[13].display_name	Fourier series
concepts[14].id	https://openalex.org/C50522688
concepts[14].level	1
concepts[14].score	0.0
concepts[14].wikidata	https://www.wikidata.org/wiki/Q189833
concepts[14].display_name	Economic growth
concepts[15].id	https://openalex.org/C77805123
concepts[15].level	1
concepts[15].score	0.0
concepts[15].wikidata	https://www.wikidata.org/wiki/Q161272
concepts[15].display_name	Social psychology
concepts[16].id	https://openalex.org/C192562407
concepts[16].level	0
concepts[16].score	0.0
concepts[16].wikidata	https://www.wikidata.org/wiki/Q228736
concepts[16].display_name	Materials science
concepts[17].id	https://openalex.org/C162324750
concepts[17].level	0
concepts[17].score	0.0
concepts[17].wikidata	https://www.wikidata.org/wiki/Q8134
concepts[17].display_name	Economics
concepts[18].id	https://openalex.org/C159985019
concepts[18].level	1
concepts[18].score	0.0
concepts[18].wikidata	https://www.wikidata.org/wiki/Q181790
concepts[18].display_name	Composite material
concepts[19].id	https://openalex.org/C15744967
concepts[19].level	0
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q9418
concepts[19].display_name	Psychology
keywords[0].id	https://openalex.org/keywords/uniqueness
keywords[0].score	0.7133362293243408
keywords[0].display_name	Uniqueness
keywords[1].id	https://openalex.org/keywords/mathematics
keywords[1].score	0.7039598226547241
keywords[1].display_name	Mathematics
keywords[2].id	https://openalex.org/keywords/generalization
keywords[2].score	0.6706339716911316
keywords[2].display_name	Generalization
keywords[3].id	https://openalex.org/keywords/convergence
keywords[3].score	0.6421574950218201
keywords[3].display_name	Convergence (economics)
keywords[4].id	https://openalex.org/keywords/matrix
keywords[4].score	0.6282780170440674
keywords[4].display_name	Matrix (chemical analysis)
keywords[5].id	https://openalex.org/keywords/relaxation
keywords[5].score	0.6239610910415649
keywords[5].display_name	Relaxation (psychology)
keywords[6].id	https://openalex.org/keywords/initial-value-problem
keywords[6].score	0.593838632106781
keywords[6].display_name	Initial value problem
keywords[7].id	https://openalex.org/keywords/applied-mathematics
keywords[7].score	0.5681359767913818
keywords[7].display_name	Applied mathematics
keywords[8].id	https://openalex.org/keywords/absolute-convergence
keywords[8].score	0.5176551938056946
keywords[8].display_name	Absolute convergence
keywords[9].id	https://openalex.org/keywords/cauchy-distribution
keywords[9].score	0.48459041118621826
keywords[9].display_name	Cauchy distribution
keywords[10].id	https://openalex.org/keywords/iterative-method
keywords[10].score	0.4809969365596771
keywords[10].display_name	Iterative method
keywords[11].id	https://openalex.org/keywords/mathematical-analysis
keywords[11].score	0.4531524181365967
keywords[11].display_name	Mathematical analysis
keywords[12].id	https://openalex.org/keywords/mathematical-optimization
keywords[12].score	0.20615047216415405
keywords[12].display_name	Mathematical optimization
keywords[13].id	https://openalex.org/keywords/fourier-series
keywords[13].score	0.06820836663246155
keywords[13].display_name	Fourier series
language	en
locations[0].id	pmh:oai:arXiv.org:2312.10891
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2312.10891
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2312.10891
locations[1].id	doi:10.48550/arxiv.2312.10891
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2312.10891
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5101439947
authorships[0].author.orcid	https://orcid.org/0000-0003-3924-0987
authorships[0].author.display_name	Xuehua Li
authorships[0].author_position	first
authorships[0].raw_author_name	Li, Xuehua
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5076646271
authorships[1].author.orcid	https://orcid.org/0000-0002-2116-363X
authorships[1].author.display_name	Cairong Chen
authorships[1].author_position	last
authorships[1].raw_author_name	Chen, Cairong
authorships[1].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2312.10891
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	A generalization of the relaxation-based matrix splitting iterative method for solving the system of generalized absolute value equations
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10792
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	0.9993000030517578
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1703
primary_topic.subfield.display_name	Computational Theory and Mathematics
primary_topic.display_name	Matrix Theory and Algorithms
related_works	https://openalex.org/W571281153, https://openalex.org/W2949403936, https://openalex.org/W4301247218, https://openalex.org/W2050111419, https://openalex.org/W2898988421, https://openalex.org/W1974759277, https://openalex.org/W3012869132, https://openalex.org/W1968696210, https://openalex.org/W2889455557, https://openalex.org/W4287264870
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2312.10891
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2312.10891
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2312.10891
primary_location.id	pmh:oai:arXiv.org:2312.10891
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2312.10891
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2312.10891
publication_date	2023-12-18
publication_year	2023
referenced_works_count	0
abstract_inverted_index.a	2, 18, 84
abstract_inverted_index.By	0
abstract_inverted_index.On	36, 78
abstract_inverted_index.by	44
abstract_inverted_index.is	34, 115
abstract_inverted_index.of	20, 60, 76
abstract_inverted_index.to	63, 72
abstract_inverted_index.we	50, 82, 96
abstract_inverted_index.RMS	22
abstract_inverted_index.and	6, 58, 65, 87, 103
abstract_inverted_index.can	70
abstract_inverted_index.few	85
abstract_inverted_index.for	26, 55, 91
abstract_inverted_index.new	3, 86
abstract_inverted_index.one	38
abstract_inverted_index.our	68
abstract_inverted_index.the	7, 11, 21, 28, 37, 46, 56, 61, 73, 79, 112
abstract_inverted_index.GRMS	101
abstract_inverted_index.give	51
abstract_inverted_index.into	10
abstract_inverted_index.show	110
abstract_inverted_index.some	41, 52, 92, 104
abstract_inverted_index.that	67, 111
abstract_inverted_index.(RMS)	15
abstract_inverted_index.GAVEs	64
abstract_inverted_index.hand,	39, 81
abstract_inverted_index.other	80
abstract_inverted_index.prove	66
abstract_inverted_index.using	45
abstract_inverted_index.value	31
abstract_inverted_index.(GRMS)	23
abstract_inverted_index.GAVEs.	77
abstract_inverted_index.matrix	4, 13
abstract_inverted_index.method	16, 25, 69, 102, 114
abstract_inverted_index.obtain	83
abstract_inverted_index.unique	74
abstract_inverted_index.unlike	40
abstract_inverted_index.weaker	88
abstract_inverted_index.(GAVEs)	33
abstract_inverted_index.between	100
abstract_inverted_index.solving	27
abstract_inverted_index.Cauchy's	47
abstract_inverted_index.absolute	30
abstract_inverted_index.converge	71
abstract_inverted_index.existing	42, 93, 105
abstract_inverted_index.methods,	43
abstract_inverted_index.methods.	94, 106
abstract_inverted_index.momentum	8
abstract_inverted_index.proposed	113
abstract_inverted_index.solution	62, 75
abstract_inverted_index.theorems	99
abstract_inverted_index.Moreover,	95
abstract_inverted_index.equations	32
abstract_inverted_index.establish	97
abstract_inverted_index.existence	57
abstract_inverted_index.iterative	24
abstract_inverted_index.numerical	108
abstract_inverted_index.principle	49
abstract_inverted_index.proposed.	35
abstract_inverted_index.splitting	5, 14
abstract_inverted_index.comparison	98
abstract_inverted_index.conditions	54, 90
abstract_inverted_index.efficient.	116
abstract_inverted_index.sufficient	53
abstract_inverted_index.uniqueness	59
abstract_inverted_index.Preliminary	107
abstract_inverted_index.convergence	48, 89
abstract_inverted_index.experiments	109
abstract_inverted_index.generalized	29
abstract_inverted_index.acceleration	9
abstract_inverted_index.incorporating	1
abstract_inverted_index.relaxed-based	12
abstract_inverted_index.generalization	19
abstract_inverted_index.\cite{soso2023},	17
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	2
citation_normalized_percentile