Univariate Function Decomposition via Tridiagonal Vector Enhanced Multivariance Products Representation (TVEMPR)

Abstract

This work is devoted to the decomposition of a univariate function by using very recently developed Tridiagonal Vector Enhanced Multivariance Products Representation (TVEMPR). To this end the target function is expressed as a bilinear form over the power vector of the independent variable and the function's coefficient vector. Both vectors are composed of denumerable infinite number of elements. The power vector of the independent variable is decomposed via Tridiagonal Vector Enhanced Multivariance Products Representation. The core matrix of the decomposition contains a 2×2 type left uppermost block as the only nonzero agent. Then the bilinear form, and therefore the function can be expressed thoroughly to get a decomposition as a linear combination of certain functions which are in fact derived from the original target function. This is the simplest case. Some other but complicated cases which start with multi outer products are left to future works. The support vectors have been chosen as proportional to certain power vectors of some given parameters to proceed from rather simplicity.