The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Metin Demiralp - One of the best experts on this subject based on the ideXlab platform.
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block Tridiagonal Matrix enhanced multivariance products representation btmempr
Journal of Mathematical Chemistry, 2018Co-Authors: Zeynep Gundogar, Metin DemiralpAbstract:The basic aim of this work is to design a new Tridiagonal Matrix enhanced multivariance products representation (TMEMPR) which uses not Cartesian vectors but matrices as the support entities. What we obtain after the construction of the representation has been a singular value decomposition like structure where the core Matrix becomes a block Tridiagonal Matrix in contrast to the diagonal and Tridiagonal Matrix structures of the singular value decomposition of matrices and TMEMPR respectively. We have used support matrices in the construction and not directly orthogonality of the constructed support matrices but block orthogonality which means the mutual ortho normality of the columns of produced support matrices. Certain confirmative implementations finalize the paper.
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weighted Tridiagonal Matrix enhanced multivariance products representation wtmempr for decomposition of multiway arrays applications on certain chemical system data sets
Journal of Mathematical Chemistry, 2017Co-Authors: Evrim Korkmaz Ozay, Metin DemiralpAbstract:This work focuses on the utilization of a very recently developed decomposition method, weighted Tridiagonal Matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a Tridiagonal Matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.
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recursive bivariate enhanced multivariance products representation to Tridiagonalize arrowheaded matrices Tridiagonal Matrix enhanced multivariance products representation tmempr with weight considerations
AIP Conference Proceedings, 2017Co-Authors: Ayla Okan, Metin DemiralpAbstract:In this work, we focus on designing a transformation from arrowheaded to Tridiagonal matrices by using a novel method “Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR)”. We have quite recently developed “Arrow-headed Enhanced Multivariance Products Representation for A Kernel” decomposition method which produces arrowheaded core matrices. However Tridiagonal Matrix forms are preferred in most scientific fields. “Arrowheaded Enhanced Multivariance Products Representation for a Kernel (AEMPRK)”, decomposing a linear univariate integral operator and its kernel which can be expressed as a finite sum of binary products composed of univariate functions, was developed and improved by M. Demiralp and his research group. In principal, TMEMPR, can Tridiagonalize any type Matrix, so the arrowheaded ones, by using only identity Matrix weights or some other Matrix weights. We especially emphasize on weight issues here in this work and show certain very interesting reductive features of TMEMPR.
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The Influence of Initial Vector Selection on Tridiagonal Matrix Enhanced Multivariance Products Representation
2014 International Conference on Mathematics and Computers in Sciences and in Industry, 2014Co-Authors: Cosar Gözökirmizi, Metin DemiralpAbstract: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. The initial vectors of the recursion of the formulation are two normalized support vectors. This work focuses on implementation of the method and the choice of these support vectors.
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Infinite Vector Decomposition in Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) Perspective
2014 International Conference on Mathematics and Computers in Sciences and in Industry, 2014Co-Authors: N.a. Baykara, Metin DemiralpAbstract: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 functions such that the remainder was becoming to have less rank as we proceed until no bivariate component remains. Here however, we focus on denumerably infinite vectors and first appropriately fold them to semi infinite matrices with finite number of denumerable infinite rows, then decompose the resulting infinite matrices via TMEMPR, and at the final stage we unfold each additive term of the representation via unique inversion of the folding procedure we use.
Li Jie-hong - One of the best experts on this subject based on the ideXlab platform.
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Inverse Problem of Generalized Eigenvalue for Nonnegtive Symmetric Tridiagonal Matrix
Journal of Tianjin University of Science and Technology, 2020Co-Authors: Li Jie-hongAbstract:we discuss a inverse problem of generalized eigenvalue for nonnegtive symmetric Tridiagonal Matrix by giving part of eigenvalues and corresponding eigenvectors.And we give the sufficient conditions for solubility of this problem.
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On the Generalized Eigenvalue of Nonegtive Period Symmetric Tridiagonal Matrix Inverse Problem
Journal of Tangshan College, 2020Co-Authors: Li Jie-hongAbstract:The paper discusses the generalized eigenvalue of the nonegtive period symmetric Tridiagonal Matrix inverse problem by giving part of eigenvalues and corresponding eigenvectors.
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On the period symmetric Tridiagonal Matrix inverse problem of generalized eigenvalue
Pure and Applied Mathematics, 2020Co-Authors: Li Jie-hongAbstract:We discuss the period symmetric Tridiagonal Matrix inverse problem of generalized eigenvalue by giving part of eigenvectors and corresponding eigenvectors, and we obtain the theorem for the solubility of this problem. We also discuss the algorithms for solving the problem.
H A Yamani - One of the best experts on this subject based on the ideXlab platform.
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the analytic inversion of any finite symmetric Tridiagonal Matrix
Journal of Physics A, 1997Co-Authors: H A Yamani, M S AbdelmonemAbstract:We use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal Matrix H. The Green's function is the inverse of the infinite symmetric Tridiagonal Matrix (H-zI). By calculating the inverse of the finite symmetric Tridiagonal Matrix we can find the analytical form of the inverse of the finite symmetric Tridiagonal Matrix, .
Akiyoshi Wakatani - One of the best experts on this subject based on the ideXlab platform.
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a parallel scheme for solving a Tridiagonal Matrix with pre propagation
Lecture Notes in Computer Science, 2003Co-Authors: Akiyoshi WakataniAbstract:A Tridiagonal Matrix for ADI method can be solved by Gaussian elimination with iterations of three substitutions, two of which need to be carefully parallelized in order to achieve high performance. We propose a parallel scheme for these substitutions (first-order recurrence equations) with scalability to the problem size and our experiment shows that it achieves \(\frac{P}{2.1}\) speedup with P processors.
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PVM/MPI - A Parallel Scheme for Solving a Tridiagonal Matrix with Pre-propagation
Lecture Notes in Computer Science, 2003Co-Authors: Akiyoshi WakataniAbstract:A Tridiagonal Matrix for ADI method can be solved by Gaussian elimination with iterations of three substitutions, two of which need to be carefully parallelized in order to achieve high performance. We propose a parallel scheme for these substitutions (first-order recurrence equations) with scalability to the problem size and our experiment shows that it achieves \(\frac{P}{2.1}\) speedup with P processors.
M S Abdelmonem - One of the best experts on this subject based on the ideXlab platform.
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the analytic inversion of any finite symmetric Tridiagonal Matrix
Journal of Physics A, 1997Co-Authors: H A Yamani, M S AbdelmonemAbstract:We use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal Matrix H. The Green's function is the inverse of the infinite symmetric Tridiagonal Matrix (H-zI). By calculating the inverse of the finite symmetric Tridiagonal Matrix we can find the analytical form of the inverse of the finite symmetric Tridiagonal Matrix, .
