Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:A3L-A
Session:
Number:A3L-A3
Accurate and Robust Inverse Cholesky Factorization
Takeshi Ogita, Shin’ichi Oishi,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
In this paper, an algorithm of matrix factorization based on Cholesky factorization for extremely ill-conditioned matrices is proposed. The Cholesky factorization is widely used for solving a system of linear equations whose coefficient matrix is symmetric and positive definite. However, it sometimes breaks down by the presence of an imaginary root due to the accumulation of rounding errors. To overcome this, a robust algorithm named inverse Cholesky factorization is investigated, which never breaks down as long as the matrix is symmetric and positive definite. Numerical results are also presented.