A new highly convergent Monte Carlo method for matrix computations1Supported by The Royal Society (UK), partially supported by the NATO Grant R406/02640 and by the Ministry of Science and Education of Bulgaria under Grants no. I 501 and no. MM 449.1

I.T. Dimov and V.N. Alexandrov

Mathematics and Computers in Simulation (MATCOM), 1998, vol. 47, issue 2, 165-181

Abstract: In this paper a second degree iterative Monte Carlo method for solving systems of linear algebraic equations and matrix inversion is presented. Comparisons are made with iterative Monte Carlo methods with degree one. It is shown that the mean value of the number of chains N, and the chain length T, required to reach given precision can be reduced. The following estimate on N is obtained: N=Nc/(cN+bN1/2c)2, where Nc is the number of chains in the usual degree one method. In addition it is shown that b>0 and that NKeywords: Monte Carlo method; Matrix computations; Convergence; Eigenvalues; Convergent iterative process; Parallel computation (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:47:y:1998:i:2:p:165-181

DOI: 10.1016/S0378-4754(98)00101-3

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