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 2012

Fingerprint

Multivariate Functions
Homogeneous Polynomials
Multivariate Polynomials
Smooth function
Tensor
Polynomial
Coefficient

Keywords

  • Frames
  • Homogeneous polynomials
  • Sampling
  • Symmetric tensors

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sampling of homogeneous polynomials and approximating multivariate functions. / Datta, Somantika; Howard, Stephen; Cochran, Douglas.

In: Advances in Pure and Applied Mathematics, Vol. 3, No. 4, 12.2012, p. 421-441.

Research output: Contribution to journalArticle

Datta, Somantika ; Howard, Stephen ; Cochran, Douglas. / Sampling of homogeneous polynomials and approximating multivariate functions. In: Advances in Pure and Applied Mathematics. 2012 ; Vol. 3, No. 4. pp. 421-441.
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