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.

Includes bibliographical references and index.

Introduction -- 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 -- Appendix A: Elements of algebra and analysis -- Appendix B: Unitary and orthogonal decompositions -- Appendix C: Kronecker product of metrices -- Appendix D: Fixed point principles -- Appendix E: Sylvester operators -- Appendix F: Lyapunov operators -- Appendix G: Lyapunov-like operators -- Appendix H: Notation.

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