Scaled simplicial approximation for the inversion of Gaussian RBF expansions

This paper addresses the problem of inverting the nonlinear functions that are approximated using an expansion in terms of Gaussian radial basis functions (GRBFs). The inverse problem posed is: find the solutions {x|f(x)ε Q} of the equation f(x) ε Q, where Q is a set of interest in the range of f, or, briefly, to find the set S=f^-1(Q). The paper proposes a computational framework based on simplicial approximation for tackling this problem. An algorithm is proposed in this framework that exploits the scaling properties of GRBFs, and some implementation details and simulation results are presented