An approach of orthogonalization within the Gram-Schmidt algorithm

被引：4

作者：

Rivaz, A. ^{[1
]}

Moghadam, M. Mohseni ^{[1
]}

Sadeghi, D. ^{[1
]}

Kermani, H. Momenaee ^{[1
]}

机构：

[1] Shahid Bahonar Univ Kerman, Fac Math & Comp, Dept Appl Math, Kerman 7616914111, Iran

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 02期

关键词：

Gram-Schmidt algorithm; Loss of orthogonality; Ill-conditioned matrix; Optimized Gram-Schmidt algorithm; Reorthogonalization;

D O I：

10.1007/s40314-016-0389-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider the variants of Gram-Schmidt such as Classical Gram-Schmidt and Modified Grain-Schmidt algorithms. It is shown that for problems of dimension more than two the round-off error of operation q(1)(T)q(2) has more propagation in both of algorithms. To cure this difficulty we will present an algorithm, namely Optimized Modified Gram-Schmidt algorithm. Numerical examples indicate the accuracy of this algorithm. We show that this method can improve the loss of orthogonality of the orthogonalization in some ill-conditioned cases.

引用

页码：1250 / 1262

页数：13

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