In this book a general perturbation theory for matrix algebraic equations is presented. Local and non-local perturbation bounds are derived for general types of matrix equations as well as for the most important equations arising in linear algebra and control theory. A large number of examples, tables and figures is included in order to illustrate the perturbation techniques and bounds.
. The first book in this field
. Can be used by a variety of specialists
. Material is self-contained
. Results can be used in the development of reliable computational algorithms
. A large number of examples and graphical illustrations are given
. Written by prominent specialists in the field
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2 Perturbation problems.
3 Problems with explicit solutions.
4 Problems with implicit solutions.
5 Lyapunov majorants.
6 Singular problems.
7 Perturbation bounds.
8 General Sylvester equations.
9 Specific Sylvester equations.
10 General Lyapunov equations.
11 Lyapunov equations in control theory.
12 General quadratic equations.
13 Continuoustime Riccati equations.
14 Coupled Riccati equations.
15 General fractionalafine equations.
16 Symmetric fractionalafine equations.
A Elements of algebra and analysis.
B Unitary and orthogonal decompositions.
C Kronecker product of matrices.
D Fixed point principles.
E Sylvester operators.
F Lyapunov operators.
G Lyapunovlike operators.