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https://doi.org/10.3336/gm.53.2.12

GMRES on tridiagonal block Toeplitz linear systems

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


Puni tekst: engleski pdf 138 Kb

str. 437-447

preuzimanja: 337

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Sažetak

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.

Ključne riječi

GMRES; tridiagonal block Toeplitz matrix; linear system

Hrčak ID:

214483

URI

https://hrcak.srce.hr/214483

Datum izdavanja:

30.12.2018.

Posjeta: 731 *