When modified Gram–Schmidt generates a well‐conditioned set of vectors

摘要: In this paper, we show why the modified Gram-Schmidt algorithm generates a well-conditioned set of vectors. This result holds under assumption that initial matrix is not 'too ill-conditioned' in way quantified. As consequence if two iterations are performed, resulting produces whose columns orthogonal up to machine precision. Finally, illustrate through numerical experiment sharpness our result.