Convergence analysis of accurate inverse Cholesky factorization

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概要

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• This paper is concerned with factorization of symmetric and positive definite matrices which are extremely ill-conditioned. Recently, Ogita and Oishi derived an iterative algorithm for an accurate inverse matrix factorization based on Cholesky factorization for such ill-conditioned matrices. We analyze the behavior of the algorithm in detail and explain its convergency by the use of numerical error analysis. Main analysis is that each iteration reduces the condition number of a preconditioned matrix by a factor around the relative rounding error unit until convergence, which is consistent with the existing numerical results.

著者

• Ogita Takeshi

  Tokyo Woman's Christian University

• Yanagisawa Yuka

  Tokyo Woman's Christian University

関連論文

• Convergence analysis of accurate inverse Cholesky factorization
• A fast verified automatic integration algorithm using double exponential formula

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