A note on the growth factor in Gaussian elimination for generalized Higham matrices

The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and \(\mathrm{i}=\sqrt{-1}\) is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-05
Main Authors: Hou-biao, Li, Qian-Ping, Guo, Xian-Ming Gu
Format: Article
Language:English
Subjects:
Gaussian elimination
Growth factors
Mathematical analysis
Matrix methods
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and \(\mathrm{i}=\sqrt{-1}\) is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.
ISSN:2331-8422