
This article is cited in 1 scientific paper (total in 1 paper)
A parallel implementation of the matrix cross approximation method
D. A. Zheltkov^{a}, E. E. Tyrtyshnikov^{b} ^{a} Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^{b} Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow
Abstract:
The matrix cross approximation method is a fast method based on lowrank matrix approximations with complexity $O((m+n)r^2)$ arithmetic operations. Its main feature consists in the following: if a matrix is not given as an array but is given as a function of two integer arguments, then this method allows one to compute the lowrank approximation of the given matrix by evaluating only $O((m+n)r)$ values of this function. However, if the matrix is extremely large or the evaluation of its elements is computationally expensive, then such an approximation becomes timeconsuming. For such cases, the performance of the method can be improved via parallelization. In this paper we propose an efficient parallel algorithm for the case of an equal computational cost for the evaluation of each matrix element.
Keywords:
lowrank matrix approximations, matrix cross approximation method, parallel algorithms
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UDC:
519.6 Received: 13.05.2015
Citation:
D. A. Zheltkov, E. E. Tyrtyshnikov, “A parallel implementation of the matrix cross approximation method”, Vychisl. Metody Programm., 16:3 (2015), 369–375
Citation in format AMSBIB
\Bibitem{ZheTyr15}
\by D.~A.~Zheltkov, E.~E.~Tyrtyshnikov
\paper A parallel implementation of the matrix cross approximation method
\jour Vychisl. Metody Programm.
\yr 2015
\vol 16
\issue 3
\pages 369375
\mathnet{http://mi.mathnet.ru/vmp548}
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I. V. Oferkin, D. A. Zheltkov, E. E. Tyrtyshnikov, A. V. Sulimov, D. K. Kutov, V. B. Sulimov, “Evaluation of the docking algorithm based on tensor train global optimization”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:4 (2015), 83–99

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