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.