AN ALGORITHM FOR COMPUTING THE PERRON ROOT OF A NONNEGATIVE IRREDUCIBLE MATRIX by PRAKASH CHANCHANA
نویسنده
چکیده
CHANCHAN, PRAKASH. An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. (Under the direction of Carl D. Meyer.) 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. AN ALGORITHM FOR COMPUTING THE PERRON ROOT OF A NONNEGATIVE IRREDUCIBLE MATRIX by PRAKASH CHANCHANA A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy APPLIED MATHEMATICS Raleigh, North Carolina 2007
منابع مشابه
Some results on the block numerical range
The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.
متن کاملA Numerical Algorithm on the Computation of the Stationary Distribution of a Discrete Time Homogenous Finite Markov Chain
The transition matrix, which characterizes a discrete time homogeneous Markov chain, is a stochastic matrix. A stochastic matrix is a special nonnegative matrix with each row summing up to 1. In this paper, we focus on the computation of the stationary distribution of a transition matrix from the viewpoint of the Perron vector of a nonnegative matrix, based on which an algorithm for the station...
متن کاملEla a Note on Generalized Perron Complements of Z-matrices∗
The concept of the Perron complement of a nonnegative and irreducible matrix was introduced by Meyer in 1989 and it was used to construct an algorithm for computing the stationary distribution vector for Markov chains. Here properties of the generalized Perron complement of an n×n irreducible Z-matrixK are considered. First the result that the generalized Perron complements of K are irreducible...
متن کاملEla a Parallel Algorithm for Computing the Group Inverse via Perron Complementation∗
A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T , where T ∈ Rn×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement t...
متن کاملA parallel algorithm for computing the group inverse via Perron complementation
A parallel algorithm is presented for computing the group inverse of a singular M–matrix of the form A = I − T , where T ∈ Rn×n is irreducible and stochastic. The algorithm is constructed in the spirit of Meyer’s Perron complementation approach to computing the Perron vector of an irreducible nonnegative matrix. The asymptotic number of multiplication operations that is necessary to implement t...
متن کامل