Enclosing solutions of linear equations

被引：8

作者：

Rohn, J ^{[2
]}

Rex, G

机构：

[1] Acad Sci Czech Republic, Inst Comp Sci, Prague, Czech Republic

[2] Charles Univ Prague, Fac Math & Phys, Prague, Czech Republic

[3] Univ Leipzig, Inst Math, D-04109 Leipzig, Germany

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1998年 / 35卷 / 02期

关键词：

linear equations; enclosure; interval-free; finite termination;

D O I：

10.1137/S0036142996299423

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is shown that Rump's method for enclosing solutions of linear equations can be reformulated in an interval-free form and that the underlying inclusion result can be proved by elementary means without using Brouwer's fixed-point theorem. A sufficient condition on Rump's "inflation parameter" epsilon is given under which finite termination occurs. Also, a more general modified algorithm is studied for which the number of iterations can be expressed by an explicit formula.

引用

页码：524 / 539

页数：16

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