Abstract
Multivariate simplex splines are capable of approximating non-linear input-output mappings with great accuracy, as can neural networks. A new method is proposed which combines the best qualities of simplex splines and polynomial neural networks while circumventing their drawbacks. The new method generates mappings which are continuously differentiable, use a stable polynomial basis, and are not restricted to contiguous configurations of simplices. The method is shown to perform equally well or better than both polynomial neural networks and standard simplex splines for a highly non-linear identification problem. An iterative polynomial order optimization scheme has been applied to all three methods to increase their performance. Finally the setup of the new method creates the opportunity for simplex vertex optimization using standard (gradient) methods.
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