Subdirect Sums of $ GSD{D_1} $ matrices-Reference-Cited by-同舟云学术

Subdirect Sums of $ GSD{D_1} $ matrices

Published:2024 Issue:6 Volume:32 Page:3989-4010
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Qi Jiaqi,Wang Yaqiang

Abstract

<abstract><p>The class of generalized $ SD{D_1} \; \left({GSD{D_1}} \right) $ matrices is a new subclass of $ H $-matrices. In this paper, we focus on the subdirect sum of $ GSD{D_1} $ matrices, and some sufficient conditions to ensure that the subdirect sum of $ GSD{D_1} $ matrices with strictly diagonally dominant $ \left({SDD} \right) $ matrices is in the class of $ GSD{D_1} $ matrices are given. Moreover, corresponding examples are given to illustrate our results.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference20 articles.

1. S. M. Fallat, C. R. Johnson, Subdirect sums and positivity classes of matrices, Linear Algebra Appl., 288 (1999), 149–173. https://doi.org/10.1016/s0024-3795(98)10194-5

2. R. Bru, F. Pedroche, D. B. Szyld, Subdirect sums of $S$-strictly diagonally dominant matrices, Electron. J. Linear Algebra, 15 (2006), 201–209. https://doi.org/10.13001/1081-3810.1230

3. R. Bru, F. Pedroche, D. B. Szyld, Subdirect sums of nonsingular $M$-matrices and of their invers-e, Electron. J. Linear Algebra, 13 (2005), 162–174. https://doi.org/10.13001/1081-3810.1159

4. A. Frommer, D. B. Szyld, Weighted max norms, splittings, and overlapping additive Schwarz iterations, Numer. Math., 83 (1999), 259–278. https://doi.org/10.1007/s002110050449

5. R. Bru, F. Pedroche, D. B. Szyld, Additive Schwarz iterations for Markov chains, SIAM J. Matrix Anal. Appl., 27 (2005), 445–458. https://doi.org/10.1137/040616541