标量情况下多点迭代法的精确松弛

Serge E. Miheev
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引用次数: 2

摘要

基于极小性原理和适用于单点迭代法的精确松弛也适用于多点迭代法。它加速并稳定了迭代过程。提出了一种简便有效的n点迭代法精确松弛计算算法,并进行了验证。该算法可以绕过求n次多项式的根的问题。该算法的计算价格易于在迭代开始前估计。这允许优先指定精确松弛应用的便利性。当n = 2时,即对于割线法,简化了精确松弛的计算公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exact relaxation of multi point iterative methods in scalar case
Based on the principle of minimality and well applicable for one-point iterative methods the exact relaxation can be adapted also to multi point ones. It accelerates and stabilizes iterative process. Simple effective algorithm to calculate exact relaxation for n-points iterative method is proposed and justified. The algorithm allows to circumvent the problem to find roots of polynomial with degree n > 2. The algorithm calculation price is easy estimated before iteration beginning. This lets a priory to specify expediency of the exact relaxation application. If n = 2 i.e. for secant method, the calculational formulas of exact relaxation are reduced.
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