Constructing Approximations to Bivariate Piecewise-Smooth Functions
<|reference_start|>Constructing Approximations to Bivariate Piecewise-Smooth Functions: 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.<|reference_end|>
@article{levin2024constructing,
    title={Constructing Approximations to Bivariate Piecewise-Smooth Functions},
    author={David Levin (Tel Aviv University)},
    journal={arXiv preprint arXiv:2405.06462},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06462},
    primaryClass={math.NA cs.NA}
}