Numerical methods and programming
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Num. Meth. Prog.: Year: Volume: Issue: Page: Find

 Num. Meth. Prog., 2015, Volume 16, Issue 3, Pages 369–375 (Mi vmp548)

A parallel implementation of the matrix cross approximation method

D. A. Zheltkova, E. E. Tyrtyshnikovb

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 low-rank 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 low-rank 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: low-rank matrix approximations, matrix cross approximation method, parallel algorithms.

Full text: PDF file (182 kB)
UDC: 519.6

Citation: D. A. Zheltkov, E. E. Tyrtyshnikov, “A parallel implementation of the matrix cross approximation method”, Num. Meth. Prog., 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 Num. Meth. Prog. \yr 2015 \vol 16 \issue 3 \pages 369--375 \mathnet{http://mi.mathnet.ru/vmp548} 

• http://mi.mathnet.ru/eng/vmp548
• http://mi.mathnet.ru/eng/vmp/v16/i3/p369

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. 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