A Class of Diagonal Transformation Methods for the Computation of the Spectral Radius of a Nonnegative Irreducible Matrix

1981 ◽  
Vol 18 (4) ◽  
pp. 693-704 ◽  
Author(s):  
Wolfgang Bunse
Keyword(s):  
Spectral Radius ◽  
Irreducible Matrix ◽  
Transformation Methods ◽  
Nonnegative Irreducible Matrix

scholarly journals Non-negative integral matrices with given spectral radius and controlled dimension

2021 ◽  
pp. 1-24
Author(s):  
MEHDI YAZDI
Keyword(s):  
Spectral Radius ◽  
Positive Real Number ◽  
Algebraic Integer ◽  
Log P ◽  
Irreducible Matrix ◽  
Positive Real ◽  
Shift Of Finite Type ◽  
Primitive Matrix ◽  
Integral Matrices ◽  
Perron Number

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

scholarly journals A Numerical Algorithm on the Computation of the Stationary Distribution of a Discrete Time Homogenous Finite Markov Chain

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Di Zhao ◽  
Hongyi Li ◽  
Donglin Su
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Discrete Time ◽  
Transition Matrix ◽  
Stochastic Matrix ◽  
Nonnegative Matrix ◽  
Homogeneous Markov Chain ◽  
Irreducible Matrix ◽  
Nonnegative Irreducible Matrix ◽  
Perron Vector

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 stationary distribution is proposed. The algorithm can also be used to compute the Perron root and the corresponding Perron vector of any nonnegative irreducible matrix. Furthermore, a numerical example is given to demonstrate the validity of the algorithm.

Imputation Via Copula and Transformation Methods, With Applications to Financial and Economic Data

2010 ◽  
Author(s):  
Yangyong Zhang ◽  
Craig A. Friedman ◽  
Jinggang Huang ◽  
Wenbo Cao
Keyword(s):  
Economic Data ◽  
Transformation Methods
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