Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.
This is a post-peer reviewed electronic version of an article published in Applied Mathematics and Computation. A link to the published version is provided below.
Field of Research
010201 Approximation Theory and Asymptotic Methods
Socio Economic Objective
970101 Expanding Knowledge in the Mathematical Sciences
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