Accession Number : ADA193709

Title :   Ill-Posed Problems and Integral Equations.

Descriptive Note : Final rept. 1 Aug 83-14 Oct 87,

Corporate Author : DELAWARE UNIV NEWARK DEPT OF MATHEMATICAL SCIENCES

Personal Author(s) : Nashed, M Z ; Eggermont, Paul P

PDF Url : ADA193709

Report Date : 22 Feb 1988

Pagination or Media Count : 18

Abstract : This document addresses 5 substantial problems in the theory and numerical analysis of ill-posed problems and integral equations: (1) Collocation, and Galerkin methods for Volterra and Abel equations of the first kind; (2) Galerkin and collocation methods for nonlinear Abel-Volterra integral equations on the half-line and on a finite interval; (3) a new approach to classification and regularization of ill-posed operator equations, and quantification of ill-posedness; (4) operator external problems in the theory of compensation and representation of control systems; (5) constrained least-squares solutions of linear inclusions and singular control problems in Hilbert space. New notions of bivariational and singular variational derivatives for functionals are also studies. They will be applied to extend the von Mises calculus for statistical functionals and its applications to robustness and approximation theorems. Keyboards: Multivalued linear mappings; Kernel functions.

Descriptors :   *INTEGRAL EQUATIONS, *NUMERICAL ANALYSIS, CALCULUS, COMPENSATION, CONTROL SYSTEMS, HILBERT SPACE, INTERVALS, KERNEL FUNCTIONS, LEAST SQUARES METHOD, OPERATORS(MATHEMATICS), SOLUTIONS(GENERAL), THEOREMS, THEORY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE