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- W4386002610 abstract "The paper is devoted to the problem of finding bivariate tensor-product spline (or similar) functions that approximate gridded data in the least-squares sense. We propose to apply a low rank approximation of matrices to the data, to find the result by solving a sequence of univariate fitting problems that can be handled efficiently. This can be seen as a generalization of the method proposed by Georgieva and Hofreither (2017) that combines cross approximation (which is a particular method for low rank matrix approximation) with spline interpolation. While the algorithm yields the best least-squares approximation after r steps, where r denotes the rank of the data matrix, terminating it earlier yields a low-rank approximation, which often provides a sufficient level of accuracy. We also present a stopping criterion (based on a lower error estimate) that allows to use the method efficiently in the situation when the required number of degrees of freedom is not known in advance." @default.
- W4386002610 created "2023-08-20" @default.
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- W4386002610 date "2024-03-01" @default.
- W4386002610 modified "2023-10-12" @default.
- W4386002610 title "Using low-rank approximations of gridded data for spline surface fitting" @default.
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- W4386002610 doi "https://doi.org/10.1016/j.cam.2023.115519" @default.
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