Acceleration and theoretical analysis of algorithms in terms of discrete integrable systems of hungry type

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740110
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Shibaura Institute of Technology (2014); Tokyo University of Science (2012-2013)
• Principal Investigator: FUKUDA Akiko 芝浦工業大学, システム理工学部, 助教 (70609297)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 離散可積分系 / 固有値 / 離散戸田方程式 / 超離散化 / 保存量 / 中心多様体 / 収束次数 / 原点シフト

Outline of Final Research Achievements

In the previous study, we have designed two algorithms: the dhLV algorithm for computing eigenvalues of nonsymmetric banded matrix based on the discrete hungry Lotka-Volterra (dhLV) system, and the dhToda algorithm for computing eigenvalues of totally nonnegative matrix based on the discrete hungry Toda (dhToda) equation.
In this study, for these algorithms, we incorporate the technique for faster convergence, and clarify rounding errors, global convergence, local convergence and convergence rate. It is also clarified that the eigenvectors can be computed efficiently.

Free Research Field

応用可積分系