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Constructing Approximations to Bivariate Piecewise-Smooth Functions.
- Source :
-
Axioms (2075-1680) . Jul2024, Vol. 13 Issue 7, p428. 12p. - Publication Year :
- 2024
-
Abstract
- This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *APPROXIMATION algorithms
*FUNCTION spaces
*SET functions
*SPLINES
*GEOMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 178692293
- Full Text :
- https://doi.org/10.3390/axioms13070428