Selected Nonlinear Matrix Equations

The aim of this book is to present results about
nonlinear matrix equations, which can be useful to
anyone with interest in matrix equations. This book
will also give ideas to graduate students working on
matrix equations or in numerical linear algebra.

In this book four types of nonlinear matrix
equations are considered: Nonsymmetric Algebraic
Riccati Equation, for which it is shown, that when
the coefficient matrices form an irreducible M-
matrix, there exists a second positive solution, the
form of the second positive solution and how to find
it is also specified.
Second type is Nonsymmertic Matrix Riccati
Differential Equation - it is shown, that when the
coefficient matrices form a nonsingular M-matrix or
an irreducible singular M-matrix the equation has a
global solution and for a wide range of initial
values the global solution converges to the stable
equilibrium solution.

In the second part of the book the plus and minus
equations are considered. An iterative method
approximating the maximal positive definite solution
is analyzed and the underlying reason for the speed
up of convergence is revealed.

Autorentext

Sandra Fital-Akelbek, Ph.D.: Mathematics. Assistant Professor at Weber State University, USA

Klappentext

The aim of this book is to present results about nonlinear matrix equations, which can be useful to anyone with interest in matrix equations. This book will also give ideas to graduate students working on matrix equations or in numerical linear algebra.In this book four types of nonlinear matrix equations are considered: Nonsymmetric Algebraic Riccati Equation, for which it is shown, that when the coefficient matrices form an irreducible M-matrix, there exists a second positive solution, the form of the second positive solution and how to find it is also specified.Second type is Nonsymmertic Matrix Riccati Differential Equation - it is shown, that when the coefficient matrices form a nonsingular M-matrix or an irreducible singular M-matrix the equation has a global solution and for a wide range of initial values the global solution converges to the stable equilibrium solution. In the second part of the book the plus and minus equations are considered. An iterative method approximating the maximal positive definite solution is analyzed and the underlying reason for the speed up of convergence is revealed.