Constructing Approximations to Bivariate Piecewise-Smooth Functions

David Levin

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arXiv · 2405.06462

Constructing Approximations to Bivariate Piecewise-Smooth Functions

David Levin

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Abstract

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a 3-corner. The given data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve.

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David Levin. 2024-05-10. Constructing Approximations to Bivariate Piecewise-Smooth Functions. https://arxiv.org/abs/2405.06462

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