Iterative solution methods

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.

Title from publisher's bibliographic system (viewed on 01 Feb 2016).

Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- Acknowledgments -- Direct Solution Methods -- 1.1 Introduction: Networks and Structures -- 1.2 Gaussian Elimination and Matrix Factorization -- 1.3 Range and Nullspace -- 1.4 Practical Considerations -- 1.5 Solution of Tridiagonal Systems of Equations -- Exercises -- References -- Theory of Matrix Eigenvalues -- 2.1 The Minimal Polynomial -- 2.2 Selfadjoint and Unitary Matrices -- 2.3 Matrix Equivalence (Similarity Transformations) -- 2.4* Normal and H-Normal Matrices -- Exercises -- References -- Positive Definite Matrices, Schur Complements, and Generalized Eigenvalue Problems -- 3.1 Positive Definite Matrices -- 3.2 Schur Complements -- 3.3 Condition Numbers -- 3.4* Estimates of Eigenvalues of Generalized Eigenvalue Problems -- 3.5 Congruence Transformations -- 3.6 Quasisymmetric Matrices -- Exercises -- References -- Reducible and Irreducible Matrices and the Perron-Frobenius Theory for Nonnegative Matrices -- 4.1 Reducible and Irreducible Matrices -- 4.2 Gershgorin Type Eigenvalue Estimates -- 4.3 The Perron-Frobenius Theorem -- 4.4 Rayleigh Quotient and Numerical Range -- 4.5* Some Estimates of the Perron-Fr…