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Algorithms for optimal discontinuous piecewise linear and constant $ L\sb 2$ 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
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 $ {L_2}$ 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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Keywords: Best fits, adjustable nodes
Article copyright: © Copyright 1994 American Mathematical Society