Accurate downdating of a modified Gram-Schmidt QR decomposition
Given \({z^T \choose \widetilde X} = X\), \(\widetilde{X} = \widetilde{Q} {R\choose 0}\). Find \(R\), such that \(X = Q {R \choose 0}\). A new algorithm for this process (which the authors call downdating) is presented. The relationship of the process to full Householder QR decomposition is explored and then used to derive an algorithm that improves the Gram-Schmidt downdating algorithm. Results of numerical tests are given. These results show that the proposed algorithm produces more accurate results than the usual algorithm for certain ill-conditioned problems.
scientific article; zbMATH DE number 881192