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Original scientific paper
https://doi.org/10.3336/gm.53.2.12

GMRES on tridiagonal block Toeplitz linear systems

Reza Doostaki   ORCID icon orcid.org/0000-0001-8861-1604 ; Young Researchers and Elite Club, Kahnooj Branch, Islamic Azad University, Kerman, Iran

Fulltext: english, pdf (138 KB) pages 437-447 downloads: 231* cite
APA 6th Edition
Doostaki, R. (2018). GMRES on tridiagonal block Toeplitz linear systems. Glasnik matematički, 53 (2), 437-447. https://doi.org/10.3336/gm.53.2.12
MLA 8th Edition
Doostaki, Reza. "GMRES on tridiagonal block Toeplitz linear systems." Glasnik matematički, vol. 53, no. 2, 2018, pp. 437-447. https://doi.org/10.3336/gm.53.2.12. Accessed 4 Dec. 2021.
Chicago 17th Edition
Doostaki, Reza. "GMRES on tridiagonal block Toeplitz linear systems." Glasnik matematički 53, no. 2 (2018): 437-447. https://doi.org/10.3336/gm.53.2.12
Harvard
Doostaki, R. (2018). 'GMRES on tridiagonal block Toeplitz linear systems', Glasnik matematički, 53(2), pp. 437-447. https://doi.org/10.3336/gm.53.2.12
Vancouver
Doostaki R. GMRES on tridiagonal block Toeplitz linear systems. Glasnik matematički [Internet]. 2018 [cited 2021 December 04];53(2):437-447. https://doi.org/10.3336/gm.53.2.12
IEEE
R. Doostaki, "GMRES on tridiagonal block Toeplitz linear systems", Glasnik matematički, vol.53, no. 2, pp. 437-447, 2018. [Online]. https://doi.org/10.3336/gm.53.2.12

Abstracts
We study the generalized minimal residual (GMRES) method for solving tridiagonal block Toeplitz linear system Ax=b with m × m diagonal blocks. For m=1, these systems becomes tridiagonal Toeplitz linear systems, and for m> 1, A becomes an m-tridiagonal Toeplitz matrix. Our first main goal is to find the exact expressions for the GMRES residuals for b=(B1,0,…, 0)T, b=(0,…, 0, BN)T, where B1 and BN are m-vectors. The upper and lower bounds for the GMRES residuals were established to explain numerical behavior. The upper bounds for the GMRES residuals on tridiagonal block Toeplitz linear systems has been studied previously in [1]. Also, in this paper, we consider the normal tridiagonal block Toeplitz linear systems. The second main goal is to find the lower bounds for the GMRES residuals for these systems.

Keywords
GMRES; tridiagonal block Toeplitz matrix; linear system

Hrčak ID: 214483

URI
https://hrcak.srce.hr/214483

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