COLLECTIVELY COMPACT OPERATOR APPROXIMATIONS. LECTURES PRESENTED JULY-AUGUST 1967.
STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
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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. Author
- Theoretical Mathematics