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On the Monte Carlo Matrix Computations on Intel MIC Architecture

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Cybernetics and Information Technologies
Special Issue With Selected Papers From The Workshop “Two Years Avitohol: Advanced High Performance Computing Applications 2017

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1. Alexandrov, V. N., O. A. Esquivel-Flores. Towards Monte Carlo Preconditioning Approach and Hybrid Monte Carlo Algorithms for Matrix Computations. - Computers & Mathematics with Applications, Vol. 70, 2015, Issue 11, pp. 2709-2718. ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2015.08.03510.1016/j.camwa.2015.08.035Open DOISearch in Google Scholar

2. Alexandrov, V., A. Karaivan o v a. Parallel Monte Carlo Algorithms for Sparse SLAE Using MPI. - In: J. Dongarra, E. Luque, T. Margalef, Eds. LNCS. Vol. 1697. Springer, 1999, pp. 283-290.Search in Google Scholar

3. Alexandrov, V., O. Esquivel-Flores, S. Ivanovska, A. Karaivan o v a. On the Preconditioned Quasi-Monte Carlo Algorithm for Matrix Computations. - In: LNCS. Vol. 9374. Springer, 2015, pp. 163-171.Search in Google Scholar

4. Atanassov, E. I. On the Discrepancy of the Halton Sequences. - Mathematica Balkanica, Vol. 18, 2004, Fasc. 1-2, pp. 15-32.Search in Google Scholar

5. Atanassov, E. I. A New Efficient Algorithm for Generating the Scrambled Sobol’ Sequence. Numerical Methods and Applications. - In: LNCS. Vol. 2542. Springer-Verlag. 2003, pp. 83-90.Search in Google Scholar

6. Atanassov, E., T. Gurov, S. Ivanovska, A. Karaivan o v a. Parallel Monte Carlo on Intel MIC Architecture. - Procedia Computer Science, Vol. 108, 2017, pp. 1803-1810. https://doi.org/10.1016/j.procs.2017.05.14910.1016/j.procs.2017.05.149Open DOISearch in Google Scholar

7. Atanassov, E., T. Gurov, A. Karaivanova, S. Ivanovska, M. Durchova, D. Dimitrov. On the Parallelization Approaches for Intel MIC Architecture. - In: AIP Conf. Proc. 1773, 070001, 2016. http://dx.doi.org/10.1063/1.496498310.1063/1.4964983Search in Google Scholar

8. Boisvert, R. F. et al. Matrix Market: A Web Resource for Test Matrix Collections. - In: R. F. Boisvert, Ed. Quality of Numerical Software. IFIP Advances in Information and Communication Technology. Boston, Springer, MA, 1997, pp. 125-137.Search in Google Scholar

9. Caflisch, R. Monte Carlo and Quasi-Monte Carlo Methods. - Acta Numerica, Vol. 7, 1998, pp. 1-49.10.1017/S0962492900002804Search in Google Scholar

10. Curtiss, J. H. Monte Carlo Methods for the Iteration of Linear Operators. - J. of Math. Physics, Vol. 32, 1954, pp. 209-232.10.1002/sapm1953321209Search in Google Scholar

11. Danilov, D., S. Ermakov, J. H. Halton. Asymptotic Complexity of Monte Carlo Methods for Solving Linear Systems. - J. of Stat. Planning and Inference, Vol. 85, 2000, pp. 5-18.10.1016/S0378-3758(99)00060-9Search in Google Scholar

12. Davis, T. A., Y. H u. SuiteSparse Matrix Collection. - ACM Transactions on Mathematical Software (TOMS), Vol. 38, 2011, No 1, p. 1. www.cise.ufl.edu/research/sparse/matrices/10.1145/2049662.2049663Search in Google Scholar

13. Dimov, I., V. Alexandrov, A. Karaivan o v a. Resolvent Monte Carlo Methods for Linear Algebra Problems. - Math. and Comp. in Simulations, Vol. 55, 2001, pp. 25-36.10.1016/S0378-4754(00)00243-3Search in Google Scholar

14. Dimov, I., A. Karaivan o v a. Parallel Computations of Eigenvalues Based on a Monte Carlo Approach. - Monte Carlo Methods and Applications, Vol. 4, 1998, No 1, pp. 33-52.10.1515/mcma.1998.4.1.33Search in Google Scholar

15. Fathi, B., B. Liu, V. Alexandr o v. Mixed Monte Carlo Parallel Algorithms for Matrix Computation. - In: LNCS. Vol. 2330. Springer, 2002, pp. 609-618.Search in Google Scholar

16. Forsythe, G., R. Leible r. Matrix Inversion by a Monte Carlo Method. - Math. Tables and other Aids to Computation, Vol. 4, 1950, pp. 127-147.10.2307/2002508Search in Google Scholar

17. Grote, M., M. Hagemann. SPAI: SParse Approximate Inverse Preconditioner, Spaidoc. - Pdf paper in the SPAI, Vol. 3, 2006, p. 1.Search in Google Scholar

18. Hammersley, J., D. Handscom b. Monte Carlo Methods. New York, London, Sydney, John Wiley & Sons, 1964.10.1007/978-94-009-5819-7Search in Google Scholar

19. Halton, J. H. Sequential Monte Carlo. - Proceedings of the Cambridge Philosophical Society, Vol. 58, Part 1, 1962, pp. 57-78.10.1017/S0305004100036227Search in Google Scholar

20. Halton, J. H. Sequential Monte Carlo Techniques for the Solution of Linear System. - IAM J. of Sci. Comp., Vol. 9, 1994, pp. 213-257.10.1007/BF01578388Search in Google Scholar

21. Huckle, T., et al. An Efficient Parallel Implementation of the MSPAI Preconditioner. - Par. Computing, Vol. 36, 2010, No 5-6, pp. 273-284.10.1016/j.parco.2009.12.007Search in Google Scholar

22. Karaivanova, A. Quasi-Monte Carlo Methods for Some Linear Algebra Problems. Convergence and Complexity. - Serdica J. of Comp., Vol. 4, 2010, pp. 58-72.10.55630/sjc.2010.4.57-72Search in Google Scholar

23. Kroese, D. P., T. Taimre, Z. I. Botev. Handbook of Monte Carlo Methods. John Wiley & Sons, 2011.10.1002/9781118014967Search in Google Scholar

24. Mascagni, M., A. Karaivan o v a. Matrix Computations Using Quasirandom Sequences. - In: LNCS. Vol. 1988. Springer, 2001, pp. 552-559.Search in Google Scholar

25. Mascagni, M., A. Karaivan o v a. A Parallel Quasi-MCM for Computing Extremal Eigenvalues. - In: MCQMCMs 2000. Springer, 2002, pp. 369-380.10.1007/978-3-642-56046-0_25Search in Google Scholar

26. Sobol, I. Monte Carlo Numerical Methods. Moscow, Nauka, 1973 (in Russian).Search in Google Scholar

27. Stoykov, S., E. Atanassov, S. Margenov. Efficient Sparse Matrix-Matrix Multiplication for Computing Periodic Responses by Shooting Method on Intel Xeon Phi. - In: AIP Conference Proceedings, 1773, 110012, 2016. http://dx.doi.org/10.1063/1.496501610.1063/1.4965016Search in Google Scholar

28. Straßburg, J., V. N. Alexandr o v. Enhancing Monte Carlo Preconditioning Methods for Matrix Computations. - In: Proc. of ICCS 2014, pp. 1580-1589.10.1016/j.procs.2014.05.143Search in Google Scholar

29. Vajargah, B. F. A New Algorithm with Maximal Rate Convergence to Obtain Inverse Matrix. -Applied Mathematics and Computation, Vol. 191, 2007, No 1, pp. 280-286. http://dx.doi.org/10.1016/j.amc.2007.02.08510.1016/j.amc.2007.02.085Open DOISearch in Google Scholar

30. Wasow, W. A Note on the Inversion of Matrices by Random Walks. - Math. Tables and other Aids to Computation, Vol. 6, 1952, pp. 78-81.10.1090/S0025-5718-1952-0055033-2Search in Google Scholar

31. We stlake, J. A Handbook of Numerical Matrix Inversion and Solution of Linear Equations. New York, J. Wiley & Sons, 1968.Search in Google Scholar

32. Yimu, J., K. Zizhuo, P. Q. Yu, S. Yanpeng, K. Jiangbang, H. Wei. A Cloud Computing Service Architecture of a Parallel Algorithm Oriented to Scientific Computing with CUDA and Monte Carlo. - Cybernetics and Information Technologies, Vol. 13, 2013, Special Issue, pp. 153-166.10.2478/cait-2013-0046Search in Google Scholar

33. Intel® Xeon Phi™ Coprocessor Instruction Set Architecture Reference Manual. https://software.intel.com/sites/default/files/forum/278102/327364001en.pdfSearch in Google Scholar

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