Constrained variational refinement

Scott N. Kersey
2009 Journal of Computational and Applied Mathematics  
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
more » ... ults are applied to closed periodic curves, open curves with various boundary conditions, and (approximate) Hermite interpolation.
doi:10.1016/j.cam.2008.03.033 fatcat:raceuivlm5dd3g7axtlm25ptsa