@article{oai:sucra.repo.nii.ac.jp:00013621,
 author = {桑島, 豊 and 重原, 孝臣},
 issue = {2},
 journal = {日本応用数理学会論文誌, Transactions of the Japan Society for Industrial and Applied Mathematics},
 month = {},
 note = {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., 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/, text, application/pdf},
 pages = {89--115},
 title = {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)},
 volume = {15},
 year = {2005},
 yomi = {クワジマ, ユタカ and シゲハラ, タカオミ}
}