Improved error bounds for linear systems with H-matrices

Atsushi Minamihata; Kouta Sekine; Takeshi Ogita; Siegfried M. Rump; Shin'ichi Oishi

doi:10.1587/nolta.6.377

Special Section on Recent Progress in Verified Numerical Computations

Improved error bounds for linear systems with H-matrices

Atsushi Minamihata, Kouta Sekine, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

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Keywords: linear system, error bound, H-matrix, verified numerical computations

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2015 Volume 6 Issue 3 Pages 377-382

DOI https://doi.org/10.1587/nolta.6.377

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Abstract

Improved componentwise error bounds for approximate solutions of linear systems are derived in the case where the coefficient of a given linear system is an H-matrix. One of the error bounds presented in this paper proves to be tighter than the existing error bound, which is effective especially for ill-conditioned cases. Numerical experiments are performed to illustrate the effect of the improvements.

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