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This paper discusses the orthogonalisation process in Gram - Schimdt algorithms. Four variants of gram-schmidt process are presented, and the relation between matrix size and running time for computation is also discussed. Loss of orthogonality of the computed vectors in gram - schmidt process can be reducted to be close to the machine precision level by reorthogonalisation. Theorithically, the loss of orthogonality is bounded, and it is true that reorthogonalisation in gram ...
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