Globally Optimal Multivariate Splines: Optimizing B-coefficient and vertex coordinates of simplex splines using interval analysis

In applications like model identification accurate methods for data approximation are required. Multivariate simplex B-splines form a class of nonlinear function approximators capable of approximating scattered data. Simplex B-splines are piecewise polynomials defined on a triangulation. Currently, data approximation using simplex B-splines is done by optimizing the B-coefficients of the spline function, without optimizing the triangulation. Triangulation optimization is a standing problem of function approximation using simplex splines. Recently the Interspline was presented, an interval extension of simplex splines with interval B-coefficients defined on a triangulation with interval vertices. Using Intersplines guaranteed global optimization of the vertices of the triangulation and the B-coefficients is possible. However, until now this method was only applicable for optimization of univariate and bivariate linear simplex B-splines on very specific triangulations. The contribution of this work is a method for guaranteed global optimization of vertices and B-coefficients of $n$-variate linear simplex splines with zero order continuity on general triangulations. This partly solves the triangulation optimization problem for simplex splines. Using this method data can be approximated more accurately, while the triangulation stays the same size.

Subject

Simplex Splines
Interval Analysis
Model Identification

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http://resolver.tudelft.nl/uuid:b37dba92-2059-4306-a5ee-3e69eac8de38

Embargo date

2017-11-28

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Student theses

Document type

master thesis

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