Nonnegative Matrices in the Mathematical Sciences

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SIAM, 1994 - Mathematics - 340 pages
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Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993. Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices.
  

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Contents

Nonnegative Matrices
24
Semigroups of Nonnegative Matrices
63
Symmetric Nonnegative Matrices
87
Generalized InversePositivity 1 Introduction
112
Irreducible Monotonicity
115
Generalized InversePositivity
117
Generalized Monomial Matrices _
122
Set Monotonicity
127
Nonnegativity and Convergence
181
Singular Linear Systems
196
Exercises
203
Notes
207
Finite Markov Chains 1 Introduction
211
Examples
214
Classical Theory of Chains 218
218
Modern Analysis of Chains
226

Exercises
128
Notes
130
MMatrices 1 Introduction
132
Nonsingular MMatrices
133
MMatrices and Completely Monotonie Functions
142
General MMatrices
147
Exercises
158
Notes
161
Iterative Methods for Linear Systems 1 Introduction ч
165
A Simple Example
167
Basic Iterative Methods
170
The SOR Method
172
Exercises
237
Notes
241
InputOutput Analysis in Economics 1 Introduction _
243
A Simple Application _ _
246
The Open Model
251
The Closed Model
258
Exercises
265
Notes
268
The Linear Complementarity Problem
271
Supplement 19791993
299
References
322
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