2024-03-29T07:34:15Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00009073
2023-01-16T03:54:36Z
320:321:322
Recent Developments in Algorithms for Solving Dense Eigenproblems (II) : Multishift QR Algorithms
密行列固有値解法の最近の発展(II) : マルチシフトQR法
山本, 有作
25459
Yamamoto, Yusaku
25460
The QR algorithm is one of the most reliable and widely used methods to compute the eigenvalues of symmetric and nonsymmetric matrices. However, it is not straightforward to execute the QR algorithm efficiently on modern architectures such as processors with hierarchical memory or parallel computers because of its inherent sequential nature and low data reference locality. To overcome this difficulty, Bai & Demmel proposed the multishift QR algorithm in 1989 and this idea has been greatly expanded since then. In this paper, we introduce the basic theory of the multishift QR algorithm and review recent developments to improve its efficiency, such as the two-tone QR algorithm, aggressive early deflation and the fully-pipelined multishift QR algorithm. Directions for future research are also discussed.
(サーベイ,行列・固有値問題の解法とその応用,<特集>平成18年研究部会連合発表会) (Survey,Algorithms for Matrix/Eigenvalue Problems and their Application,<Special Issue> "Joint Symposium of JSIAM Activity Groups 2006")
journal article
日本応用数理学会
2006-12-25
application/pdf
日本応用数理学会論文誌
4
16
507
534
http://hdl.handle.net/2237/10841
09172246
https://nagoya.repo.nii.ac.jp/record/9073/files/yamamoto_989.pdf
jpn
http://ci.nii.ac.jp/naid/110006197075/
日本応用数理学会
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