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In this paper, we consider the mixed and componentwise condition numbers fora linear function of the solution to the linear least squares problem withequality constrains (LSE). We derive the explicit expressions of the mixed andcomponentwise condition numbers through the dual techniques. The sharp upperbounds for the derived mixed and componentwise condition numbers are obtained,which can be estimated efficiently by means of the classical Hager-Highamalgorithm for estimating matrix one-norm during using the generalized QRfactorization method for solving LSE. The numerical examples show that thederived condition numbers can give sharp perturbation bounds, on the other handnormwise condition numbers can severely overestimate the relative errorsbecause normwise condition numbers ignore the data sparsity and scaling.

Mixed and componentwise condition numbers for a linear function of the solution of the linear least squares problem with equality constrains