Adaptive Cross Approximation of Multivariate Functions

In this article we present and analyze a new scheme for the approximation of multivariate functions ( d =3,4) by sums of products of univariate functions. The method is based on the Adaptive Cross Approximation (ACA) initially designed for the approximation of bivariate functions. To demonstrate the...

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Bibliographic Details
Published in:Constructive approximation Vol. 34; no. 2; pp. 149 - 179
Main Author: Bebendorf, M.
Format: Journal Article
Language:English
Published: New York Springer-Verlag 01.10.2011
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Dimensionality reduction
41A80
15A69
41A63
Data compression
Adaptive cross approximation
ISSN:0176-4276, 1432-0940
Online Access:Get full text
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Summary:In this article we present and analyze a new scheme for the approximation of multivariate functions ( d =3,4) by sums of products of univariate functions. The method is based on the Adaptive Cross Approximation (ACA) initially designed for the approximation of bivariate functions. To demonstrate the linear complexity of the schemes, we apply it to large-scale multidimensional arrays generated by the evaluation of functions.
ISSN:0176-4276
1432-0940
DOI:10.1007/s00365-010-9103-x