Perturbation Theory for the Rank-Deficient Equality Constrained Least Squares Problem
Musheng Wei · SIAM Journal on Numerical Analysis · 1992
This paper presents perturbation theory for the equality constrained least squares problem $\min _{f \in S} \| {Kf - g} \|2$ with $S = \{ f:\| {Lf - h} \|_2 = \min _{y \in C^n } \| {Ly - h} \|_2\} $ (LSE), in which L and $(\begin{array}{*{20}c} L \\ K \\ \end{array} )$ may not be of full rank. The analysis generalizes the results of Eldén [4]. Perturbation theorems for the LSE problem are proved. Numerical experiments are also given to verify the error bounds.