Item type |
レポート / Report(1) |
公開日 |
2022-06-09 |
タイトル |
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言語 |
en |
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タイトル |
NII Technical Report (NII-2020-001E):A Stabilized GMRES Method for Solving Underdetermined Least Squares Problems |
言語 |
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言語 |
eng |
キーワード |
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言語 |
ja |
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主題Scheme |
Other |
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主題 |
テクニカルレポート |
キーワード |
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言語 |
en |
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主題Scheme |
Other |
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主題 |
Technical Report |
資源タイプ |
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資源 |
http://purl.org/coar/resource_type/c_6501 |
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タイプ |
departmental bulletin paper |
ID登録 |
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ID登録 |
10.20736/0002000369 |
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ID登録タイプ |
JaLC |
著者 |
LIAO, Zeyu
速水, 謙
保國, 惠一
YIN, Jun-Feng
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抄録 |
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内容記述タイプ |
Abstract |
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内容記述 |
Consider using the right-preconditioned generalized minimal residual (AB-GMRES) method, which is an efficient method for solving underdetermined least squares problems. Morikuni (Ph.D. thesis, 2013) showed that for some inconsistent and illconditioned problems, the iterates of the AB-GMRES method may diverge. This is mainly because the Hessenberg matrix in the GMRES method becomes very ill-conditioned so that the backward substitution of the resulting triangular system becomes numerically unstable. We propose a stabilized GMRES based on solving the normal equations corresponding to the above triangular system using the standard Cholesky decomposition. This has the effect of shifting upwards the tiny singular values of the Hessenberg matrix which lead to an inaccurate solution. Thus, the process becomes numerically stable and the system becomes consistent, rendering better convergence and a more accurate solution. Numerical experiments show that the proposed method is robust and efficient for solving inconsistent and ill-conditioned underdetermined least squares problems. The method can be considered as a way of making the GMRES stable for highly ill-conditioned inconsistent problems. |
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言語 |
en |
書誌情報 |
ja : NIIテクニカル・レポート
en : NII Technical Report
p. 1-20,
発行日 2020-03-30
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出版者 |
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言語 |
ja |
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出版者 |
国立情報学研究所 |
ISSN |
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収録物識別子タイプ |
ISSN |
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収録物識別子 |
1346-5597 |