Algorithms for optimal discontinuous piecewise linear and constant fits to continuous functions with adjustable nodes in one and two dimensions

Author:
M. J. Baines

Journal:
Math. Comp. **62** (1994), 645-669

MSC:
Primary 65D10; Secondary 41A30

DOI:
https://doi.org/10.1090/S0025-5718-1994-1223231-5

MathSciNet review:
1223231

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Abstract: In this paper a direct variational approach (with nonstandard variations) is used to generate algorithms to determine optimal *discontinuous* piecewise linear and piecewise constant fits to a continuous function of one or two variables with adjustable nodes. In the one-variable case the algorithm is fast and robust, the mesh cannot tangle, and the resulting fits are continuous a.e. In the two-variable case, on an adjustable triangular grid, the algorithm is less robust but gives good results for particular functions possessing a single steep feature. The extension to higher dimensions is straightforward.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1994-1223231-5

Keywords:
Best fits,
adjustable nodes

Article copyright:
© Copyright 1994
American Mathematical Society