An approach of orthogonalization within the Gram-Schmidt algorithm

作者：Rivaz A; Moghadam M Mohseni; Sadeghi D^*; Kermani H Momenaee

来源：COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37(2): 1250-1262.

DOI：10.1007/s40314-016-0389-6

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

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.

• 出版日期2018-5