Spectra of Multiplication Operators as a Numerical Tool

Abstract

We introduce a numerical procedure for the construction of interpolation and quadrature formulae on bounded convex regions in the plane. The construction is based on the behavior of spectra of certain multiplication operators and leads to nodes which are inside a prescribed convex region in R(2). The resulting interpolation schemes are numerically stable and the quadrature formulae have positive weights and almost (but not quite) optimal numbers of nodes. The performance of the algorithm is illustrated by several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Mar 03, 2011
Accession Number
ADA555151

Entities

People

  • B. Vioreanu
  • Vladimir Rokhlin

Organizations

  • Yale University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Complex Numbers
  • Complex Variables
  • Computer Science
  • Eigenvalues
  • Equations
  • Functional Analysis
  • Gaussian Quadrature
  • Inequalities
  • Integrals
  • Interpolation
  • Mathematics
  • Numbers
  • Numerical Analysis
  • Numerical Integration
  • Spectra
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra