A backward stability analysis of diagonal pivoting methods for solving unsymmetric tridiagonal systems without interchanges
✍ Scribed by Jennifer B. Erway; Roummel F. Marcia
- Book ID
- 102546539
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 129 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1070-5325
- DOI
- 10.1002/nla.674
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✦ Synopsis
This paper concerns the LBM T factorization of unsymmetric tridiagonal matrices, where L and M are unit lower triangular matrices and B is block diagonal with 1×1 and 2×2 blocks. In some applications, it is necessary to form this factorization without row or column interchanges while the tridiagonal matrix is formed. Bunch and Kaufman proposed a pivoting strategy without interchanges specifically for symmetric tridiagonal matrices, and more recently, Bunch and Marcia proposed pivoting strategies that are normwise backward stable for linear systems involving such matrices. In this paper, we extend these strategies to the unsymmetric tridiagonal case and demonstrate that the proposed methods both exhibit bounded growth factors and are normwise backward stable.