Least Squares Methods to Minimize Errors in a Smooth, Strictly Convex Norm on Rm Original Research Article

An algorithm for computing solutions of overdetermined systems of linear equations in n real variables which minimize the residual error in a smooth, strictly convex norm in a finite dimensional space is given. The algorithm proceeds by finding a sequence of least squares solutions of suitably modified problems. Most of the time, each iteration involves one line search for the root of a nonlinear equation, though some iterations do not have any root seeking line search. Convergence of the algorithm is proved, and computational experience on some numerical examples is also reported.