Abstract: Global Convergence Properties of the Splitting Iterations for Solving Linear Least Squares Problems

This paper deals with the splitting iterations for solving linear least squares problems with a certain positive definite splitting matrix which produce globally convergent sequences of monotonically improved approximates. Such sequences monotonically converge to the unique solution of a certain bi-level linear least squares problem, namely to that linear least squares solution, nearest the initial guess in the sense of a certain elliptic distance. As important consequences, the particular analytic expressions of global limit of the so-called Iterated Tikhonov's Regularization and the Proximal Point method sequences in general form are deduced; as well as of the sequences of certain novel approximating versions of the well-known Jacobi and Minimum Norm iteration respectively.