Preface vii1. Introduction and Review1.1 Basic symbols1.2 Quadratic forms and positive definite matrices1.2.1 Quadratic forms1.2.2 Problems involving quadratic forms1.2.3 Positive definite matrix1.2.4 Other methods to determine the positive definiteness1.3 Theorems for eigenvalues of symmetric matrices1.4 Complex inner product spaces1.5 Hermitian, unitary, and normal matrices1.6 Kronecker product and Kronecker sum2. Norms and Perturbation Analysis2.1 Vector norms2.2 Matrix norms2.3 Perturbation analysis for linear systems2.4 Error on floating point numbers3. Least Squares Problems3.1 Solution of LS problems3.2 Perturbation analysis for LS problems3.3 Orthogonal transformations3.3.1 Householder reflections3.3.2 Givens rotations3.4 An algorithm based on QR factorization3.4.1 QR factorization3.4.2 A practical algorithm for LS problems4. Generalized Inverses4.1 Moore-Penrose generalized inverse4.2 Basic properties4.3 Relation to LS problems4.4 Other generalized inverses5. Conjugate Gradient Method5.1 Steepest descent method5.1.1 Steepest descent method5.1.2 Convergence rate5.2 Conjugate gradientmethod5.2.1 Conjugate gradient method5.2.2 Basic properties5.2.3 Practical CG method5.3 Preconditioning technique6. Optimal and Superoptimal Preconditioners6.1 Introduction to optimal preconditioner6.1.1 Circulantmatrix6.1.2 Optimal preconditioner6.2 Linear operator c_U6.2.1 Algebraic properties6.2....... 全部内容请购买实物书籍
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