| 言語種別 | 英語 |
|---|---|
| 発行・発表の年月 | 2022/01 |
| 形態種別 | 学術研究論文 |
| 査読 | 査読あり |
| 標題 | Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations |
| 執筆形態 | 単著 |
| 掲載誌名 | Japan Journal of Industrial and Applied Mathematics |
| 出版社・発行元 | Springer Science and Business Media LLC |
| 巻・号・頁 | 39(1),19-74 |
| 担当区分 | 筆頭著者 , 責任著者 |
| 著者・共著者 | Shoji Itoh |
| 概要 | Abstract
In this paper, improved algorithms are proposed for preconditioned bi-Lanczos-type methods with residual norm minimization for the stable solution of systems of linear equations. In particular, preconditioned algorithms pertaining to the bi-conjugate gradient stabilized method (BiCGStab) and the generalized product-type method based on the BiCG (GPBiCG) have been improved. These algorithms are more stable compared to conventional alternatives. Further, a stopping criterion changeover is proposed for use with these improved algorithms. This results in higher accuracy (lower true relative error) compared to the case where no changeover is done. Numerical results confirm the improvements with respect to the preconditioned BiCGStab, the preconditioned GPBiCG, and stopping criterion changeover. These improvements could potentially be applied to other preconditioned algorithms based on bi-Lanczos-type methods. |
| DOI | 10.1007/s13160-021-00480-0 |
| ISSNコード | 0916-7005/1868-937X |
| PermalinkURL | https://link.springer.com/content/pdf/10.1007/s13160-021-00480-0.pdf |
| researchmap用URL | https://link.springer.com/article/10.1007/s13160-021-00480-0/fulltext.html |