Using dual techniques to derive componentwise and mixed condition numbers for a linear function of a linear least squares solution
Duality results for adjoint operators and product norms in the framework of Euclidean space are proved. It is shown how these results can be used to derive condition numbers especially when perturbations on data are measured componentwise relatively to the original data. The technique proposed is applied to obtain formulas for componentwise and mixed condition numbers for a linear function of a linear least squares solution. These expressions are closed when perturbations of the solution are measured using a componentwise norm or the infinity norm and an upper bound for the Euclidean norm is got. A numerical example is given.
scientific article; zbMATH DE number 5549603
scientific article