On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems
It is shown how the modified Gram-Schmidt algorithm can be used for constrained and weighted linear least squares problems. The equivalence between the weighted modified Gram-Schmidt algorithm and an algorithm based on a weighted Householder-like QR factorization applied to a slightly larger problem is used to explain the instability of the proposed algorithm. Also, it is shown how the orthogonality of the calculated \(Q\) from the weighted modified Gram-Schmidt can be improved by performing reorthogonalization. Finally, numerical results are given to illustrate the main features of the algorithm.
scientific article; zbMATH DE number 844662