A Unified Theoryof Conditioning for Linear Least Squares and Tikhonov Regularization Solutions
A. N. Malyshev · SIAM Journal on Matrix Analysis and Applications · 2003
We develop a unified perturbation theory for the unconstrained linear least squares problem, least squares with linear equality constraints, and least squares with quadratic inequality constraint and Tikhonov regularization solution. The computable condition numbers are exact with respect to the Frobenius norm. For the 2-norm, the computed bounds may differ from the exact condition numbers only by a factor less than $\sqrt{2}$.