Adaptive multivariate piecewise polynomial approximation

Shai Dekel; Dany Leviatan

doi:10.1117/12.503961

Adaptive multivariate piecewise polynomial approximation

Shai Dekel^*, Dany Leviatan

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Conference article › peer-review

Abstract

We survey some recent results in the theory of multivariate piecewise polynomial approximation. In the univariate case this method is equivalent to Wavelet approximation, but in the multivariate case this is no longer true, since this form of approximation is more adaptive to the geometry of the singularities of the function to be approximated. The theory possibly has applications in image compression.

Original language	English
Pages (from-to)	125-133
Number of pages	9
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5207
Issue number	1
DOIs	https://doi.org/10.1117/12.503961
State	Published - 2003
Event	Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: 4 Aug 2003 → 8 Aug 2003

Keywords

Multivariate polynomial approximation
Nonlinear approximation
Piecewise polynomial approximation

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10.1117/12.503961

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title = "Adaptive multivariate piecewise polynomial approximation",

abstract = "We survey some recent results in the theory of multivariate piecewise polynomial approximation. In the univariate case this method is equivalent to Wavelet approximation, but in the multivariate case this is no longer true, since this form of approximation is more adaptive to the geometry of the singularities of the function to be approximated. The theory possibly has applications in image compression.",

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author = "Shai Dekel and Dany Leviatan",

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AU - Leviatan, Dany

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AB - We survey some recent results in the theory of multivariate piecewise polynomial approximation. In the univariate case this method is equivalent to Wavelet approximation, but in the multivariate case this is no longer true, since this form of approximation is more adaptive to the geometry of the singularities of the function to be approximated. The theory possibly has applications in image compression.

KW - Multivariate polynomial approximation

KW - Nonlinear approximation

KW - Piecewise polynomial approximation

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U2 - 10.1117/12.503961

DO - 10.1117/12.503961

M3 - מאמר מכנס

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JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

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IS - 1

Y2 - 4 August 2003 through 8 August 2003

ER -

Adaptive multivariate piecewise polynomial approximation

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Keywords

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