An algorithm for low-rank approximation of bivariate functions using splines

DOI10.1016/j.cam.2016.03.023zbMath1348.65051OpenAlexW2186880240MaRDI QIDQ311405

Clemens Hofreither, Irina Georgieva

Publication date: 13 September 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.03.023

zbMATH Keywords

complexityalgorithmsplinesnumerical examplesspline interpolationtruncated singular value decompositionlow-rank approximationisogeometric analysisbivariate approximationcross approximationdata compression schemetensor product spline spaces

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Multidimensional problems (41A63) Spline approximation (41A15) Algorithms for approximation of functions (65D15)

Related Items (5)

Using low-rank approximations of gridded data for spline surface fitting ⋮ Sum factorization techniques in isogeometric analysis ⋮ On the error in transfinite interpolation by low-rank functions ⋮ Bivariate Hermite interpolation by a limiting case of the cross approximation algorithm ⋮ A black-box low-rank approximation algorithm for fast matrix assembly in isogeometric analysis

Uses Software

• Chebfun
• Chebfun2

Cites Work

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• Error estimates for two-dimensional cross approximation
• Best approximation by bilinear forms
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Pseudo-skeleton approximations by matrices of maximal volume
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• A theory of pseudoskeleton approximations
• A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
• On calculating with B-splines
• A literature survey of low-rank tensor approximation techniques
• Tensor Spaces and Numerical Tensor Calculus
• Stabilized rounded addition of hierarchical matrices
• An Extension of Chebfun to Two Dimensions
• Functional analysis
• A practical guide to splines.

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