実対称三重対角固有値問題の分割統治法の拡張(<特集>行列・固有値問題における線形計算アルゴリズムとその応用)

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rights: 日本応用数理学会rights: 本文データは学協会の許諾に基づきCiNiiから複製したものであるrelation: IsVersionOf: http://ci.nii.ac.jp/naid/10016594389/Divide-and-conquer (DC) is one of the fastest algorithms for eigenproblem of a large-size symmetric tridiagonal matrix (STM). In the original DC, a STM is supposed to be divided in half. In this paper, we propose an extended DC (EDC) where a STM is divided into k parts (k>2). Compared to DC, EDC requires only 3k/(2(k^2-1)) floating operation counts if k is much smaller than the matrix size. In implementation of EDC, the orthogonality among eigenvectors with nearly multiple eigenvalues is ensured by an appropriate usage of quadruple-precision floating-point number processing. We give a formula for the floating operation counts of the present implementation, whose validity is confirmed by numerical experiment.
日本応用数理学会の論文
2005-06-25