On Convergence of dqds and mdLVs Algorithms for Singular Value Computation(Theory)
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- Aishima Kensuke
- University of Tokyo
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- Matsuo Takayasu
- University of Tokyo
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- Murota Kazuo
- University of Tokyo
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- Sugihara Masaaki
- University of Tokyo
Bibliographic Information
- Other Title
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- 特異値計算のためのdqds法とmdLVs法の収束性について(理論)
- 特異値計算のためのdqds法とmdLVs法の収束性について
- トクイチ ケイサン ノ タメノ dqdsホウ ト mdLVsホウ ノ シュウソクセイ ニ ツイテ
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Abstract
Convergence theorems are established with mathematical rigour for two algorithms for the computation of singular values of bidiogonal matrices: the differential quotient difference with shift (dqds) and the modified discrete Lotka-Volterra with shift (mdLVs). Global convergence is guaranteed under a fairly general assumption on the shift, and the asymptotic rate of convergence is 1.5 for the Johnson bound shift. This result for the mdLVs algorithm is a substantial improvement of the convergence analysis by Iwasaki and Nakamura. Numerical examples support these theoretical results.
Journal
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- Transactions of the Japan Society for Industrial and Applied Mathematics
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Transactions of the Japan Society for Industrial and Applied Mathematics 17 (2), 97-131, 2007
The Japan Society for Industrial and Applied Mathematics
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Details 詳細情報について
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- CRID
- 1390282680744495360
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- NII Article ID
- 110006317521
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 8882816
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed
