Pade近似を用いた数値等角写像計算のArnoldi法による精度改善(行列・固有値問題の解法とその応用, <特集>平成17年研究部会連合発表会)

概要

論文の詳細を見る
In this paper, we consider a method for computation of numerical conformal mappings using Pade approximation. This method calculates the poles of the denominator of a Pade approximation as charge points, using the results obtained by the charge simulation method proposed by Amano et al. Although good accuracy of numerical conformal mapping can be obtained using a few charge points, the accuracy is degraded when a certain number of charge points is exceeded. In order to improve the accuracy of this method, we reduce calculations of charge points by Pade approximation to a generalized eigenvalue problem. Moreover, we construct a highly accurate unitary matrix to appear in this generalized eigenvalue problem using the Arnoldi method. Some numerical examples illustrate the efficiency of the improved method.
日本応用数理学会の論文
2005-09-25