An Extension of Divide-and-Conquer for Real Symmetric Tridiagonal Eigenproblem(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)
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- Kuwajima Yutaka
- Graduate School of Science and Engineering, Saitama University
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- Shigehara Takaomi
- Faculty of Engineering, Saitama University
Bibliographic Information
- Other Title
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- 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)
- 実対称三重対角固有値問題の分割統治法の拡張
- ジツ タイショウ 3ジュウ タイカク コユウチ モンダイ ノ ブンカツ トウチホウ ノ カクチョウ
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Abstract
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.
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 15 (2), 89-115, 2005
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
- 1390282680744030080
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- NII Article ID
- 110001888790
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- NII Book ID
- AN10367166
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- ISSN
- 09172246
- 24240982
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- NDL BIB ID
- 7409089
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- Text Lang
- ja
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- Data Source
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- JaLC
- IRDB
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed