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New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue
Abstract:In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.
Keywords:Monte Carlo method  generalized eigenvalue problem  Markov chain  resolvent matrix  QR method
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