Sampling of homogeneous polynomials and approximating multivariate functions

Somantika Datta, Stephen Howard, Douglas Cochran

Research output: Contribution to journalArticle

Abstract

Conditions for reconstruction of multivariate homogeneous polynomials from sets of sample values are introduced. In addition, it is shown that one can explicitly obtain the polynomial coefficients from the sample data by considering frames for spaces of symmetric tensors. Further, it is discussed how the reconstruction of homogeneous polynomials can be used to approximate certain smooth functions.

Original languageEnglish (US)
Pages (from-to)421-441
Number of pages21
JournalAdvances in Pure and Applied Mathematics
Volume3
Issue number4
DOIs
StatePublished - Dec 1 2012

Keywords

  • Frames
  • Homogeneous polynomials
  • Sampling
  • Symmetric tensors

ASJC Scopus subject areas

  • Mathematics(all)

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