Sampling of homogeneous polynomials and approximating multivariate functions

Somantika Datta; Stephen Howard; Douglas Cochran

doi:10.1515/apam-2012-0028

Sampling of homogeneous polynomials and approximating multivariate functions

Somantika Datta, Stephen Howard, Douglas Cochran

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	421-441
Number of pages	21
Journal	Advances in Pure and Applied Mathematics
Volume	3
Issue number	4
DOIs	https://doi.org/10.1515/apam-2012-0028
State	Published - Dec 2012

Keywords

Frames
Homogeneous polynomials
Sampling
Symmetric tensors

ASJC Scopus subject areas

General Mathematics

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title = "Sampling of homogeneous polynomials and approximating multivariate functions",

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.",

keywords = "Frames, Homogeneous polynomials, Sampling, Symmetric tensors",

author = "Somantika Datta and Stephen Howard and Douglas Cochran",

year = "2012",

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doi = "10.1515/apam-2012-0028",

language = "English (US)",

volume = "3",

pages = "421--441",

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AU - Howard, Stephen

AU - Cochran, Douglas

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AB - 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.

KW - Frames

KW - Homogeneous polynomials

KW - Sampling

KW - Symmetric tensors

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M3 - Article

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JO - Advances in Pure and Applied Mathematics

JF - Advances in Pure and Applied Mathematics

IS - 4

ER -

Sampling of homogeneous polynomials and approximating multivariate functions

Abstract

Keywords

ASJC Scopus subject areas

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