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A Newton-type algorithm for solving an extremal constrained interpolation problem

✍ Scribed by Krassimira Vlachkova

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
856 KB
Volume
7
Category
Article
ISSN
1070-5325

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✦ Synopsis

Given convex scattered data in R 3 we consider the constrained interpolation problem of finding a smooth, minimal L p -norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown.

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