Some new properties of the equality constrained and weighted least squares problem Original Research Article

In this paper, some new properties of the equality constrained and weighted least squares problem (WLSE) min short parallelW1/2(Kx−g)short parallel2 subject to Lx=h are obtained. We derive a perturbation bound based on an unconstrained least squares problem and deduce some equivalent formulae for the projectors of this unconstrained LS problem. We also present a new way to compute the minimum norm solution xWLSE of the WLSE problem by using the QR decomposition of the corresponding matrices and propose an algorithm to compute xWLSE using the QR factorizations. Some numerical examples are provided to compare different methods for solving the WLSE problem.