Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial data

A weighted least squares problem {ie863-01} with positive definite weights M and N is considered, where A ∈ R^m×n is a rank-deficient matrix, b ∈ R^m. The hereditary, computational, and global errors of a weighted normal pseudosolution are estimated for perturbed initial data, including the case where the rank of the perturbed matrix varies. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 83–95, November–December 2008.