The Novel Stochastic Bernstein Method of Functional Approximation

Abstract

The stochastic Bernstein method (not to be confused with the Bernstein polynomials) is a novel and significantly improved non-polynomial global method of signal processing that is proving very useful for interpolating and for approximating data. It arose as an obvious extension of the work of Bernstein (it preserves some of the remarkable properties of the Bernstein polynomials). However, this extension means that stochastic interpolation takes on its own properties and additionally can replace the error function by other functions such as the arctangent. The method has a free parameter sigma known as its diffusivity that can be easily optimized with adaptivity and can interpolate or approximate non-uniformly distributed input data - something that is very awkward to set up with other methods. Adaptivity can also reverse engineer the non-uniformly distributed input data that best recovers a function. This short paper provides an introduction to the new mathematical method that should find wide application in many areas of science and engineering