Tridiagonal Kernel Enhanced Multivariance Products Representation (TKEMPR) for Outer Product Sums: Arrowheading EMPR for Kernel (AEMPRK)

摘要

This work is a new extension to our a very recent work whose paper will appear in the proceedings of a very recent international conference. In that work we have developed a new version of the very recently developed decomposition method we have called "Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) for applying on the univariate integral operator kernels which are in fact bivariate functions. We specify the target bivariate function as a sum of binary products of univariate functions each of which depends on a different independent variable. These binary products can be considered as the continuos counterparts of the outer product matrices. Here, first we apply the our very recent development we have called "Tridiagonal Kernel Enhanced Multivariance Products Representation (TKEMPR)" on a binary product and show that its TKEMPR has only four additive terms. Then we use this result of a single binary product to get an expansion for a given multi binary component sum (outer product sum). We obtain the concise matrix format of singular-value-decomposition-like three factor matrix product whose kernel is in arrowhead matrix form which can be converted to a tridiagonal form. The work is at a conceptual level.