Local Spline Approximation Methods.

Abstract

The construction of explicit polynomial spline approximation operators for real-valued functions defined on intervals or on reasonably behaved sets in higher dimensions is studied. The operators take the form Qf = the summation of lambda sub i f N sub i, where the N sub i are B-splines and the lambda sub i are appropriate linear functionals. Explicit operators are found which apply to wide classes of functions including continuous or integrable functions. Moreover, the operators are local and approximate smooth functions with an accuracy comparable to best spline approximation. They can be constructed without matrix inversion, local as well as global error bounds are obtained, and some of the error bounds are free of mesh restrictions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1974
Accession Number
AD0779437

Entities

People

  • Larry L. Schumaker
  • Tom Lyche

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Construction
  • Errors
  • Intervals
  • Inversion

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra