Algorithms for optimal discontinuous piecewise linear and constant 𝐿₂ fits to continuous functions with adjustable nodes in one and two dimensions

Baines, M. J.

doi:10.1090/S0025-5718-1994-1223231-5

Algorithms for optimal discontinuous piecewise linear and constant $L_ 2$ fits to continuous functions with adjustable nodes in one and two dimensions
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Math. Comp. 62 (1994), 645-669 Request permission

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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