Convergence analysis of an algorithm for accurate inverse Cholesky factorization

Yuka Yanagisawa*, Takeshi Ogita, Shin’ichi Oishi

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

This paper is concerned with factorization of symmetric and positive definite matrices which are extremely ill-conditioned. Following the results by Rump (1990), Oishi et al. (2007, 2009) and Ogita (2010), Ogita and Oishi (2012) 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 give reasons for 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. This behavior is consistent with the numerical results.

本文言語English
ページ(範囲)461-482
ページ数22
ジャーナルJapan Journal of Industrial and Applied Mathematics
31
3
DOI
出版ステータスPublished - 2014 11 1

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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