{"title":"Structure Preserving Quaternion Biconjugate Gradient Method","authors":"Tao Li, Qing-Wen Wang","doi":"10.1137/23m1547299","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 306-326, March 2024. <br/> Abstract. This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.","PeriodicalId":49538,"journal":{"name":"SIAM Journal on Matrix Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Matrix Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1547299","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 306-326, March 2024. Abstract. This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.
期刊介绍：
The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.
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