2013•Nonlinear Theory and Its Applications IEICEOpen access

A modified algorithm for accurate inverse Cholesky factorization

Yuka Yanagisawa, Takeshi Ogita, Shin’ichi Oishi

Abstract

This paper is concerned with an inverse matrix factorization based on Cholesky factorization for ill-conditioned matrices. Recently, Ogita and Oishi derived an iterative algorithm to calculate an accurate approximate inverse of the exact Cholesky factor for such matrices. In this paper, a modified version of the algorithm is proposed. It is explained that the proposed algorithm gives more accurate results than the original one by a numerical analysis. Numerical evidence is also shown.

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Available abstract

Key concepts: Cholesky decomposition, Incomplete Cholesky factorization, Minimum degree algorithm, Inverse, Factorization, Incomplete LU factorization, Applied mathematics, Matrix (chemical analysis)