{"title":"A modified preconditioner for three-by-three block saddle point problems","authors":"Jun Li, Zhenping Li","doi":"10.1007/s13160-023-00625-3","DOIUrl":null,"url":null,"abstract":"<p>In this paper, inspired by the simplified relaxed alternating positive semi-definite splitting preconditioner (Xiong and Li in J Appl Math Comput, 2023), a modified preconditioner is established to solve the three-by-three block saddle point problems. The advantage of the modified preconditioner is that its parameters can be easy to select, which can avoid the work of the calculation of the parameters. Next, the spectral property of the preconditioned matrix with modified preconditioner is also discussed. In the end, three examples are provided to show the effectiveness of the modified preconditioner.</p>","PeriodicalId":50264,"journal":{"name":"Japan Journal of Industrial and Applied Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Japan Journal of Industrial and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13160-023-00625-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, inspired by the simplified relaxed alternating positive semi-definite splitting preconditioner (Xiong and Li in J Appl Math Comput, 2023), a modified preconditioner is established to solve the three-by-three block saddle point problems. The advantage of the modified preconditioner is that its parameters can be easy to select, which can avoid the work of the calculation of the parameters. Next, the spectral property of the preconditioned matrix with modified preconditioner is also discussed. In the end, three examples are provided to show the effectiveness of the modified preconditioner.
本文受简化松弛交替正半定分裂预条件(Xiong and Li In J applied Math computing, 2023)的启发，建立了一个改进的预条件来求解3 × 3块鞍点问题。改进后的预调节器的优点是其参数易于选择，从而避免了参数计算的工作量。其次，讨论了带修正预条件的预条件矩阵的谱性质。最后，通过三个算例说明了改进预调节器的有效性。
期刊介绍：
Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.
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