Theory and implementation of a new interpolation method based on random sampling

Abstract

In this paper we present a new method for the interpolation of functions using Feynman path integrals. It is argued that least-biased interpolations are obtained. The interpolation method is essentially numerical and an algorithm is given for determining the interpolation values. The core of the method is the identification of the interpolation values as expectation values of a random function. The expectation values are obtained by a Metropolis algorithm. The method is illustrated with a number of examples and an application in TCAD.