Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems

AbstractWe study the algebraic properties of the solutions of the equality-constrained least squares problem minfϵs ∇vKf - g∇v2 with S = {f:∇vh - Lf∇v2 = minzϵCn ∇v ∇vh - Lz∇v2} (LSE) and corresponding weighted least squares problem (WLS), in which L and lK may not be of full rank. General formulas for the solutions are given, and the algebraic relations between the LSE and the WLS solutions are obtained