Improvement of Divide and Conquer Algorithm by Twisted Factorization for Eigenvalue Decomposition(Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

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  • 固有値分解を目的としたツイスト分解法による分割統治法の改善(行列・固有値問題の解法とその応用,<特集>平成20年研究部会連合発表)
  • 固有値分解を目的としたツイスト分解法による分割統治法の改善
  • コユウチ ブンカイ オ モクテキ ト シタ ツイスト ブンカイホウ ニ ヨル ブンカツ トウチホウ ノ カイゼン

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Abstract

An algorithm which consists of a simplified D & C and twisted factorization is proposed for symmetric tridiagonal eigenvalue decomposition. The complexity is O(n^2) and the memory usage is O(n) if no cluster exists. The orthogonality can be improved by additional one step of the inverse iteration, although the classical D & C shows better one. In some numerical tests, our algorithm shows stable speed and better accuracy of the decompositions. But the orthogonality is worse than those of the classical D & C in up to three digits.

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