Challenge to Breakdown of Integrable Algorithms
Project/Area Number |
15K13457
|
Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Multi-year Fund |
Research Field |
Foundations of mathematics/Applied mathematics
|
Research Institution | Kyoto University |
Principal Investigator |
|
Co-Investigator(Kenkyū-buntansha) |
關戸 啓人 京都大学, 国際高等教育院, 特定講師 (40718235)
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
Keywords | 可積分アルゴリズム / ブレイクダウン / ランチョス法 / 連立1次方程式 / 特異点閉じ込め / 離散戸田方程式 / ブレークダウン / 連立1次方程式の反復法 / 応用可積分系 / 直交多項式 / 相対精度 / 固有値計算 / 特異値計算 / 原点シフト / 高次収束 |
Outline of Final Research Achievements |
A multistep extension of the progressive algorithm by Lanczos named the MPA is introduced and its application to linear systems is discussed. It is well-known that the Lanczos algorithm may easily breakdown caused by a division by zero of the Lanczos parameters. In this research project the Lanczos parameters are computed very accurately by using the four basic operations of arithmetic through the discrete Toda equation. Then even an ill-conditioned linear system having the Hilbert matrix as coefficient matrix is shown to be solved by using the MPA without any breakdown.
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Report
(4 results)
Research Products
(22 results)