Condition Numbers For Moore-Penrose Inverse Of Matrix And Linear Least Squares Problem

Condition number of a problem is used to measure the sensitivity of its input data to small perturbations.Studying condition number is an important aspect in matrix perturbation analysis and numerical analysis. In this field, many workers have studied and obtained a lot of useful results.Particularly,in recent twenty years,extensive attentions were paid to condition numbers of all kinds of matrix generalized inverse and condition numbers of least squares problem. At the same time, a number of classical results were obtained. The theory and methods of generalized inverse and Least-Squares problem are important basic tools in all mathematical disciplines, and have extensive applications in economics, statistics, surveying, optimization techniques, information processing, engineering techniques, operations research and so on. Therefore,studying condition number of matrix generalized inverse and least squares problem is very important not only in theory but also in practice.In this paper, we discuss condition numbers for weighted Moore-Penrose inverse (?) and weighted least squares problemrelated with weighted matrix 2-norm and weighted matrix Frobenius norm respectively, and get explicit expressions or bounds of condition number for weighted Moore-Penrbse inverse of rank-full matrix and weighted least squares problem with rank-full matrix.Moreover,we investigate condition number of some of these condition numbers(that is level-2 condition number).