An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix

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Title: An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix
Author: Chanchana, Prakash
Advisors: Carl D. Meyer, Committee Chair
Ernie L. Stitzinger, Committee Member
Zhilin Li, Committee Member
Min Kang, Committee Member
Abstract: We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz's formula with a special inverse iteration algorithm discussed in [10, Linear Algebra Appl., 15 (1976), pp 235-242]. Numerical experiments demonstrate that our algorithm is able to compute the Perron root accurately and faster than other well known algorithms; in particular, when the size of the matrix is large. The proof of convergence of our algorithm is also presented.
Date: 2007-03-09
Degree: PhD
Discipline: Applied Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/3756


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