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KAKEN_23654040seika.pdf
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クラウドコンピューティングによる大規模な離散逆問題の新しいGMRES型算法の構築
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クラウド コンピューティング ニ ヨル ダイキボナ リサン ギャクモンダイ ノ アタラシイ GMRESガタ サンポウ ノ コウチク
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Kuraudo konpyutingu ni yoru daikibona risan gyakumondai no atarashii GMRESgata sanpo no kochiku
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New GMRES algorithm for solving large scale inverse problems on a cloud computing
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野寺, 隆
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ノデラ, タカシ
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Nodera, Takashi
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慶應義塾大学理工学部・教授
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Research team head
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科研費研究者番号 : 50156212
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谷, 温之
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タニ, アツシ
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Tani, Atsushi
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慶應義塾大学理工学部・名誉教授
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Research team member
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科研費研究者番号 : 90118969
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大野, 義夫
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オオノ, ヨシオ
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Ono, Yoshio
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慶應義塾大学理工学部・名誉教授
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Research team member
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科研費研究者番号 : 20051865
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山本, 喜一
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ヤマモト, ヨシカズ
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Yamamoto, Yoshikazu
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慶應義塾大学理工学部・旧教授
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Research team member
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科研費研究者番号 : 20051873
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田村, 要造
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タムラ, ヨウゾウ
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Tamura, Yozo
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| Affiliation |
慶應義塾大学理工学部・教授
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Research team member
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科研費研究者番号 : 50171905
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2014
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科学研究費補助金研究成果報告書
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2013
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| Abstract |
離散型線形悪条件問題に対する正則化手法として、GMRES法に注目し、GMRES 法の適用過程で現れる各値を用いた制約条件を付加することで、問題の非適切性の改善を試みた研究である。
GMRES 法による正則化の過程は、(1)GMRES法によって連立1次方程式の近似解を生成し、(2)制約条件を用いて最適な近似解を決定する、2ステップに分けられる。(1)においては、GMRES 法を離散型線形悪条件問題に適用した特徴的な振る舞いについて考察し、(2)近似解決定の制約条件として、Simplified Tikhonov 閾値を提案し、数値実験により有効性を示した。
GMRES regularization method is arguably the most popular solution for linear discrete ill-posed problems. We explores different regularization methods as a means of yielding stable solutions for linear discrete ill-posed problems.
The regularization with GMRES must be implemented in two stages, which are designed to generate an approximate solution of a linear system through the use of GMRES, and to determine the most appropriate solution by using a constraint. In the first stage, particular behaviors of GMRES and preconditioned GMRES for linear discrete ill-posed problems are identified. In the second stage, a simplified Tikhonov threshold as a constraint to determine the best approximate solution is explored. Numerical experiments have been tabulated to underline the effectiveness of our proposed method.
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研究種目 : 挑戦的萌芽研究
研究期間 : 2011～2013
課題番号 : 23654040
研究分野 : 数物系科学
科研費の分科・細目 : 数学・数学一般(含確立論・統計数学)
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