An algorithm for best approximate solutions ofAx=b with a smooth strictly convex norm

Summary In this paper, overdetermined systems ofm linear equations inn unknowns are considered. With^m equipped with a smooth strictly convex norm, ·, an iterative algorithm for finding the best approximate solution of the linear system which minimizes the ·-error is given. The convergence of the algorithm is established and numerical results are presented for the case when · is anl_p norm, 1<p<.Portions of this paper are taken from the author's Ph.D. thesis at Michigan State University