Mathematical analysis of rounding errors which arise from new solvers for solving linear equations and its future developments

2017 Fiscal Year Final Research Report

• Project/Area Number: 26390136
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computational science
• Research Institution: Gifu Shotoku Gakuen University
• Principal Investigator: Abe Kuniyoshi 岐阜聖徳学園大学, 経済情報学部, 教授 (10311086)
• Co-Investigator(Kenkyū-buntansha): 石渡 恵美子 東京理科大学, 理学部第一部応用数学科, 教授 (30287958)
• Co-Investigator(Renkei-kenkyūsha): ZHANG Shao-Liang 名古屋大学, 大学院・工学研究科, 教授 (20252273) ; IKUNO Soichiro 東京工科大学, コンピュータサイエンス学部, 教授 (70318864)
• Research Collaborator: Gerard Sleijpen Utrecht University, Department of Mathematics, Professor Emeritus
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 線形方程式 / Krylov空間法 / 帰納的次元縮小法 / 前処理手法 / 丸め誤差解析 / 並列計算

Outline of Final Research Achievements

We have proposed strategies for improving the convergence speed and the accuracy of approximate solutions for the Induced Dimension Reduction(IDR)(s) method. We have derived the preconditioned IDR(s) algorithms and then examined the convergence speed and the accuracy of approximate solutions among some implementations of IDR(s). Moreover we have redesigned the conventional Krylov subspace methods for improving the convergence speed and the accuracy of approximate solutions by using the results obtained in this research. We have given strategies to parallelize preconditioning on parallel computers and then evaluated the parallel performance. We have applied our proposed the strategies to parallelize preconditioning to the application problem which arises from electromagnetics field, and then shown the effectiveness.

Free Research Field

数値計算