Report Number: CS-TR-67-76
Institution: Stanford University, Department of Computer Science
Title: Collectively compact operator approximations.
Author: Anselone, Phillip M.
Date: September 1967
Abstract: This report consists of notes based on lectures presented July-August 1967. The notes were prepared by Lyle Smith. A general approximation theory for linear and nonlinear operators on Banach spaces is presented. It is applied to numerical integration approximations of integral operators. Convergence of the operator approximations is pointwise rather than uniform on bounded sets, which is assumed in other theories. The operator perturbations form a collectively compact set, i.e., they map each bounded set into a single compact set. In the nonlinear case, Frechet differentiability conditions are also imposed. Principal results include convergence and error bounds for approximate solutions and, for linear operators, results on spectral approximations.