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In this work a new version of Enhanced Multivariance Products Representation (EMPR) is taken into consideration. Recent researches on the bivariate arrays (i.e., Matrices) have led us to a new scheme which we have called Tridiagonal Matrix Enhanced Multivariate Products Representation (TMEMPR). Therein we have been consecutively using four term EMPR on its bivariate component under different support...
We have recently shown that the operator expectation values for the quantum dynamical systems of singular Hamiltonians, cannot be expanded into temporal Maclaurin series. Depending on the nature of the system under consideration and the relevant operator, either a finite number of terms can exist while the others become infinite or the series can convergence only at the beginning of the evolution...
Enhanced Multivariance Products Representation (EMPR) is a function decomposition method formed by generalization of High Dimensional Model Representation (HDMR). EMPR may be utilized as a matrix decomposer also. The method here builds upon recursive EMPR and it decomposes a matrix into a product of three matrices: an orthonormal matrix, a rectangular tridiagonal matrix and another orthonormal matrix...
In our a previous work we have dealt with the generating function construction for representing the general term of a sequence as a moment like integral where a generating function takes the role of a weight function. We have assumed therein that the each pair of sequence elements satisfy a first order homogeneous linear recursion with variant coefficients. Then we have tried to construct ODE (s)...
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...
This work focuses on the folding and rank issues for the denumerable infinite vector foldings to denumerable semi infinite matrices. The vector to be folded is assumed to have denumerably infinite number of elements while the produced matrix is assumed to be composed of a finite number of rows and denumerably infinite number of columns as we have done in some other works of us. The vector folding...
This work is an extension of very recently developed decomposition method for matrices. That method has been called "Tridiagonal Matrix Enhanced Multivariance Product Representation, or briefly, TMEMPR. Here, in this work our ultimate goal has been taken as the decomposition of a univariate linear integral operator. Instead of this task we focus on a bivariate function since the kernel of such...
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