{"title":"Preconditioned inexact Newton-like method for large nonsymmetric eigenvalue problems","authors":"Hongyi Miao, Li Wang","doi":"10.3934/NACO.2021012","DOIUrl":null,"url":null,"abstract":"An efficiently preconditioned Newton-like method for the computation of the eigenpairs of large and sparse nonsymmetric matrices is proposed. A sequence of preconditioners based on the Broyden-type rank-one update formula are constructed for the solution of the linearized Newton system. The properties of the preconditioned matrix are investigated. Numerical results are given which reveal that the new proposed algorithms are efficient.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":"15 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algebra Control and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/NACO.2021012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
An efficiently preconditioned Newton-like method for the computation of the eigenpairs of large and sparse nonsymmetric matrices is proposed. A sequence of preconditioners based on the Broyden-type rank-one update formula are constructed for the solution of the linearized Newton system. The properties of the preconditioned matrix are investigated. Numerical results are given which reveal that the new proposed algorithms are efficient.
期刊介绍：
Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.
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