迭代方法周期性的正确实现的计算机算法的结果

1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI:10.1109/ARITH.1975.6156992

R. Klatte, C. Ullrich

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引用次数: 2

摘要

在有序集合中，在一定的假设条件下，可以证明关于单调算子生成的迭代序列的循环长度的两个基本定理。这些结果应用于不同的迭代方法，其中结论仅适用于由数值计算产生的迭代序列，如果所用的计算机算法得到适当的实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Consequences of a properly implemented computer arithmetic for periodicities of iterative methods

In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer arithmetic is properly implemented.

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1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)

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