Approximation in the extended functional tensor train format

This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function ev...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 50; no. 3
Main Authors Strössner, Christoph, Sun, Bonan, Kressner, Daniel
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2024
Springer Nature B.V
Subjects
Algorithms
Chebyshev approximation
Compressing
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Format
Functionals
Mathematical analysis
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Tensors
Visualization
Tensors
65D15
Low-rank approximation
65F55
Polynomial approximation
Multivariate functions
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Summary:This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. Compared to existing methods based on the functional tensor train format, the adaptivity of our approach often results in reducing the required storage, sometimes considerably, while achieving the same accuracy. In particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96 % compared to the algorithm from Gorodetsky et al. (Comput. Methods Appl. Mech. Eng. 347 , 59–84 2019 ).
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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-024-10140-9