Polynomial Approximation on a Sparse Grid

Scott N. Kersey

Polynomial Approximation on a Sparse Grid

Scott N. Kersey

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

We study polynomial approximation on a certain class of sparse grids that we call quasi-uniform. Using Boolean sum techniques combined with a Bernstein class of dual bases in subspaces, we construct quasi interpolants on these grids. Our construction achieves rates of approximation analogous to those on a tensor product grid, while retaining some geometric properties of Bernstein-Bezier surfaces.

Original language	American English
State	Published - May 22 2016
Event	International Conference on Approximation Theory (AT) - Duration: May 22 2016 → …

Conference

Conference	International Conference on Approximation Theory (AT)
Period	05/22/16 → …

Disciplines

Mathematics
Physical Sciences and Mathematics

Keywords

Polynomial Approximation
Sparse Grid

Access to Document

https://math.vanderbilt.edu/schumake/AT15/absfinal.pdf

Cite this

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title = "Polynomial Approximation on a Sparse Grid",

abstract = " We study polynomial approximation on a certain class of sparse grids that we call quasi-uniform. Using Boolean sum techniques combined with a Bernstein class of dual bases in subspaces, we construct quasi interpolants on these grids. Our construction achieves rates of approximation analogous to those on a tensor product grid, while retaining some geometric properties of Bernstein-Bezier surfaces.",

keywords = "Polynomial Approximation, Sparse Grid",

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year = "2016",

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language = "American English",

note = "International Conference on Approximation Theory (AT) ; Conference date: 22-05-2016",

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TY - CONF

T1 - Polynomial Approximation on a Sparse Grid

AU - Kersey, Scott N.

PY - 2016/5/22

Y1 - 2016/5/22

N2 - We study polynomial approximation on a certain class of sparse grids that we call quasi-uniform. Using Boolean sum techniques combined with a Bernstein class of dual bases in subspaces, we construct quasi interpolants on these grids. Our construction achieves rates of approximation analogous to those on a tensor product grid, while retaining some geometric properties of Bernstein-Bezier surfaces.

AB - We study polynomial approximation on a certain class of sparse grids that we call quasi-uniform. Using Boolean sum techniques combined with a Bernstein class of dual bases in subspaces, we construct quasi interpolants on these grids. Our construction achieves rates of approximation analogous to those on a tensor product grid, while retaining some geometric properties of Bernstein-Bezier surfaces.

KW - Polynomial Approximation

KW - Sparse Grid

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/219

UR - https://math.vanderbilt.edu/schumake/AT15/absfinal.pdf

M3 - Presentation

T2 - International Conference on Approximation Theory (AT)

Y2 - 22 May 2016

ER -

Polynomial Approximation on a Sparse Grid

Abstract

Conference

Disciplines

Keywords

Access to Document

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