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