Constrained Variational Refinement

Document Type

Article

Publication Date

1-15-2009

Publication Title

Journal of Computational and Applied Mathematics

DOI

10.1016/j.cam.2008.03.033

ISSN

0377-0427

Abstract

A non-uniform, variational refinement scheme is presented for computing piecewise linear curves that minimize a certain discrete energy functional subject to convex constraints on the error from interpolation. Optimality conditions are derived for both the fixed and free-knot problems. These conditions are expressed in terms of jumps in certain (discrete) derivatives. A computational algorithm is given that applies to constraints whose boundaries are either piecewise linear or spherical. The results are applied to closed periodic curves, open curves with various boundary conditions, and (approximate) Hermite interpolation.

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