Constrained Variational RefinementJournal of Computational and Applied Mathematics
AbstractA 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.
Citation InformationScott N. Kersey. "Constrained Variational Refinement" Journal of Computational and Applied Mathematics Vol. 223 Iss. 2 (2009) p. 983 - 996
Available at: http://works.bepress.com/scott_kersey/12/