New High-Accurate Numerical Methods for Inverse Problems by the Direct Computations of Integral Equations of the First Kind

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400198
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University
• Principal Investigator: Fujiwara Hiroshi 京都大学, 情報学研究科, 准教授 (00362583)
• Co-Investigator(Kenkyū-buntansha): 滝口 孝志 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群), 総合教育学群, 准教授 (50523023)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 高精度数値計算 / 数値的不安定性 / 逆問題 / 非適切問題 / 第一種積分方程式 / 多倍長計算

Outline of Final Research Achievements

We showed reliable and high-accurate numerical computations to inverse scattering problem which was known as a typical ill-posed problems in the sense of Hadamard. High-accurate discretization methods play an essential role in our method, and particularly multiple-precision arithmetic is required to reduce rounding errors. We also developed multiple-precision arithmetic environment on MATLAB which was widely used in scientific and engineering computation. The environment is faster than the official multiple-precision arithmetic environment VPA.

Free Research Field

数値解析学