Quasi Monte Carlo algorithm for computing smallest and largest generalised eigenvalues

Behrouz Fathi Vajargah, Farshid Mehrdoust

Abstract


The problem of obtaining the smallest and the largest generalised eigenvalues using quasi Monte Carlo algorithm is considered. We first study the results of Dimov and others using three algorithms based on the power method combined with Monte Carlo and quasi Monte Carlo methods for evaluating extremal eigenvalue of real matrices. We present a quasi Monte Carlo algorithm for computing both the smallest and the largest generalised eigenvalues using Sobol, Halton sequences and the rand function in Matlab. We finally compare the efficiency of three employed generators in our algorithm for different pencils.

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Keywords


Quasi Monte Carlo; Markov chian; generalized eigenvalue; resolvent matrix; discrepancy; Schur decomposition

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DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3437



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