{"title":"Two Efficient Lopsided Double-Step Methods for Solving Complex Symmetric Linear Systems","authors":"Xiao-Yong Xiao","doi":"10.1007/s40840-024-01715-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, an efficient lopsided double-step (LDS) iteration scheme is proposed to quickly solve complex symmetric linear systems, by using the real part and imaginary part of the coefficient matrix. We give detailed analysis of the spectral radius of the iteration matrix and the quasi-optimal parameter for the LDS method. In addition, a modified version of the LDS (MLDS) method is developed by using only one matrix inversion in each iteration, and the convergence properties of the MLDS method are discussed. Particularly, under suitable conditions, the convergence factors of the LDS and the MLDS methods are no more than 0.1768, and this number is less than that of many exiting methods. Numerical experiments are implemented and the results support the contention that the LDS and the MLDS methods are more efficient than several classical methods. Furthermore, we also explore the fixed parameters for the LDS and the MLDS methods in practice, and the numerical results are very satisfactory.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01715-2","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, an efficient lopsided double-step (LDS) iteration scheme is proposed to quickly solve complex symmetric linear systems, by using the real part and imaginary part of the coefficient matrix. We give detailed analysis of the spectral radius of the iteration matrix and the quasi-optimal parameter for the LDS method. In addition, a modified version of the LDS (MLDS) method is developed by using only one matrix inversion in each iteration, and the convergence properties of the MLDS method are discussed. Particularly, under suitable conditions, the convergence factors of the LDS and the MLDS methods are no more than 0.1768, and this number is less than that of many exiting methods. Numerical experiments are implemented and the results support the contention that the LDS and the MLDS methods are more efficient than several classical methods. Furthermore, we also explore the fixed parameters for the LDS and the MLDS methods in practice, and the numerical results are very satisfactory.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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