Abstract: Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two quantum algorithms to efficiently fit scattered data based on globally and compactly supported RBFs respectively. For the globally supported RBF method, the core of the quantum algorithm relies on using coherent states to calculate the radial functions and a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion. A quadratic speedup is achieved in the number of data over the classical algorithms.

Abstract: In biomechanics, geometries representing complicated organic structures are consistently segmented from sparse volumetric data or morphed from template geometries resulting in initial overclosure between adjacent geometries. In FEA, these overclosures result in numerical instability and inaccuracy as part of contact analysis. Several techniques exist to fix overclosures, but most suffer from several drawbacks. This work introduces a novel automated algorithm in an iterative process to remove overclosure and create a desired minimum gap for 2D and 3D finite element models. The RBF Network algorithm was introduced by its four major steps to remove the initial overclosure.