In this paper we consider the variants of gram-schmidt such as Classical gram-schmidt and Modified Grain-schmidtalgorithms. It is shown that for problems of dimension more than two the round-off error of operation q(...
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In this paper we consider the variants of gram-schmidt such as Classical gram-schmidt and Modified Grain-schmidtalgorithms. 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-schmidtalgorithm. 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.
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