第一種積分方程式の高精度数値計算について(科学技術計算と数値解析(多倍長科学技術計算の基礎と応用), <特集>平成17年研究部会連合発表会)

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タイトル別名
  • High-precision numerical computation of integral equations of the first kind(Scientific Computation and Numerical Analysis; Basics and Applications of Multiprecision Scientific Computation, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)
  • 第一種積分方程式の高精度数値計算について
  • ダイ1シュ セキブン ホウテイシキ ノ コウセイド スウチ ケイサン ニ ツイテ

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説明

A new method for the direct numerical computation of integral equations of the first kind, of which the integral kernels are analytic, is proposed. The basic idea of the method is based on combination of the spectral collocation method and the multiple precision computation. It gives good numerical results for the equations as far as we don't admit observation errors in the given inhomogeneous terms, and the results implies possibility of numerical analytic continuation on the multiple precision arithmetic. A new accurate rule for numerical integration is also introduced.

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