Accession Number : AD0753161

Title :   Generalized Inverses in Reproducing Kernel Spaces: an Approach to Regularization of Linear Operator Equations.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Nashed,M. Z. ; Wahba,Grace

Report Date : AUG 1972

Pagination or Media Count : 47

Abstract : In the paper a study of generalized inverses of linear operators in reproducing kernel Hilbert spaces (RKHS) is initiated. Explicit representations of generalized inverses in RKHS are obtained, and their relations to regularization of (ill-posed or poorly-conditioned) linear operator equations are explored. It is shown in particular that this approach provides a natural and effective setting for regularization problems when the operator maps one RKHS into another. Finally properties of the regularized pseudosolutions in this setting are studied. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, OPERATORS(MATHEMATICS)), HILBERT SPACE, MATRICES(MATHEMATICS), TOPOLOGY, LEAST SQUARES METHOD, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE