Condition numbers with their condition numbers for the weighted Moore-Penrose inverse and the weighted least squares solution
This paper deals with the condition numbers with their condition numbers for the weighted Moore-Penrose inverse and the weighted least squares solution of min\(_x\| Ax-b\| _M\), where \(A \in {\mathbb C}^m{}^\times{}^n\) is rank-deficient, \(x \in {\mathbb C}^n\), and \(M\) is a Hermitian matrix of order \(n\). In this respect the following topics are studied: the normwise condition number sensitivity, the componentwise condition numbers for the weighted Moore-Penrose inverse and the weighed least squares solution, and the level-2 condition numbers for componentwise condition numbers.
scientific article; zbMATH DE number 5076937