Sampling of homogeneous polynomials and approximating multivariate functions

Somantika Datta, Stephen Howard, Douglas Cochran

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Dec 2012


  • Frames
  • Homogeneous polynomials
  • Sampling
  • Symmetric tensors

ASJC Scopus subject areas

  • General Mathematics


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