Parallel mesh methods for tension splines

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Abstract

This paper addresses the problem of shape preserving spline interpolation formulated as a differential multipoint boundary value problem (DMBVP for short). Its discretization by mesh method yields a five-diagonal linear system which can be ill-conditioned for unequally spaced data. Using the superposition principle we split this system in a set of tridiagonal linear systems with a diagonal dominance. The latter ones can be stably solved either by direct (Gaussian elimination) or iterative methods (SOR method and finite-difference schemes in fractional steps) and admit effective parallelization. Numerical examples illustrate the main features of this approach.

Keywords

Shape preserving interpolation
DMBVP
Hyperbolic and thin plate tension splines
Superposition principle
Parallel Gaussian elimination
Finite-difference schemes in fractional steps

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