Chui C.K., Monk P., Wuytack L. (Eds.) Perturbation Theory for Matrix Equations

Amsterdam: Elsevier, 2003. — 443 p.The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical models together with the rounding errors done in the computational process. The perturbation bounds may further be incorporated in accuracy estimates for the solution computed in finite arithmetic. This is necessary for the development of reliable computational methods, algorithms and software from the viewpoint of modern numerical analysis.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.Perturbation problems
Problems with explicit solutions
Problems with implicit solutions
Lyapunov majorants
Singular problems
Perturbation bounds
General sylvester equations
Specific Sylvester equations
General Lyapunov equations
Lyapunov equations in control theory
General quadratic equations
Continuous-time Riccati equations
Coupled Riccati equations
General fractional-affine equations
Symmetric fractional-affine equations
Elements of algebra and analysis
Unitary and orthogonal decompositions
Kronecker product of matrices
Fixed point principles
Sylvester operators
Lyapunov operators
Lyapunov-like operators
Notation