Challenge to Breakdown of Integrable Algorithms

2017 Fiscal Year Final Research Report

• 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: Nakamura Yoshimasa 京都大学, 情報学研究科, 教授 (50172458)
• 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
• 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

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.

Free Research Field

Applied Integrable Systems