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

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)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1972
Accession Number
AD0753161

Entities

People

  • Grace Wahba
  • M. Z. Nashed

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Equations
  • Hilbert Space
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Information Retrieval

Technology Areas

  • Space