Finding the spectral radius of a large sparse non-negative matrix

Robert James Wood, Micheal O'Neill

Abstract


A comparison of methods for finding the spectral radius of a large sparse non-negative matrix. The Arnoldi method is compared with a variation of the method of Collatz [Math Zeit, 48, 221--6, 1948], this method of Collatz being always convergent when finding the spectral radius of a non-negative matrix. The advantages and disadvantages of both methods are discussed, as well as a comparison with the methods of orthogonal iteration and simultaneous iteration. Comparisons are made using flop counts.

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DOI: http://dx.doi.org/10.21914/anziamj.v48i0.117



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.