制約付き悪条件連立1次方程式の解法

概要

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The steepest descent method has been often used to solve simultaneous equations encountered in engineering problems, especially in the case of ill conditioned and the rate of convergence is very slow. If we calculate with finite figures in the method, there is a certain risk of obtaining erroneous results which do not converge to the true solution. In this paper, an algorithm for computing the constrained simultaneous equations in terms of the converged values obtained previously by the steepest descent method is described in detail. Last, two examples are presented which are the applications of this method. The one is related to simultaneous linear equations which is ill conditioned. The other is concerned in particular problem which deals with simultaneous linear equations composed of measured values for obtaining spectral transmittance of an optical filter by means of retarding potential method. In latter case, the simultaneous linear equations include some unavoidable errors.
福山大学の論文