Iterative Solution Methods

Direct Solution Methods Theory of Matrix Eigenvalues Positive Definite Matrices, Schur Complements, and Generalized Eigenvalue Problems Reducible and Irreducible Matrices and the Perron-Frobenius Theory for Nonnegative Matrices Basic Iterative Methods and Their Rates of Convergence M-Matrices, Convergent Splittings, and the SOR Method Incomplete Factorization Preconditioning Methods Approximate Matrix Inverses and Corresponding Preconditioning Methods Block Diagonal and Schur Complement Preconditionings Estimates of Eigenvalues and Condition Numbers for Preconditioned Matrices Conjugate Gradient and Lanczos-Type Methods Generalized Conjugate Gradient Methods The Rate of Convergence of the Conjugate Gradient Method Appendix - A: Matrix Norms, Inherent Errors, and Computation of Eigenvalues Appendix - B: Chebyshev Polynomials Appendix - C: Some Inequalities for Functions of Matrices Index