Stability of block LU factorization for block tridiagonal block H-matrices

Authors:
Chi-Ye Wu;Ting-Zhu Huang
Affiliations:
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, PR China and Jinan University, Shenzhen, Guangdong, 518053, PR China;School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

By a block representation of LU factorization for a general matrix introduced by Amodio and Mazzia [P. Amodio, F. Mazzia, A new approach to the backward error analysis in the LU factorization algorithm, BIT 39 (1999) 385-402], a block representation of block LU factorization for block tridiagonal block H-matrices is obtained and some properties on the factors of the factorization are presented. Perturbation theory for the block LU factorization of block tridiagonal block H-matrices is also considered. Then a rounding error analysis of the block LU factorization for block tridiagonal block H-matrices is given, and some bounds for the growth factor are proposed. Finally, a numerical example is presented to illustrate our theoretical results.