Matrix computations = 矩阵计算 / 第3版.

　　1 Matrix Multiplication Problems
　　 1.1 Basic Algorithms and Notation
　　 1.2 Exploiting Structure
　　 1.3 Block Matrices and Algorithms
　　 1.4 Vectorization and Re-Use Issues
　　2 Matrix Analysis
　　 2.1 Basic Ideas from Linear Algebra
　　 2.2 Vector Norms
　　 2.3 Matrix Norms
　　 2.4 Finite Precision Matrix Computations
　　 2.5 Orthogonality and the SVD
　　 2.6 Projections and the CS Decomposition
　　 2.7 The Sensitivity of Square Linear Systems
　　3 General Linear Systems
　　 3.1 Triangular Systems
　　 3.2 The LU Factorization
　　 3.3 Roundoff Analysis of Gaussian Elimination
　　 3.4 Pivoting
　　 3.5 Improving and Estimating Accuracy
　　4 Special Linear Systems
　　 4.1 The LDMT and LDLT Factorizations
　　 4.2 Positive Definite Systems
　　 4.3 Banded Systems
　　 4.4 Symmetric Indefinite Systems
　　 4.5 Block Systems
　　 4.6 Vandermonde Systems and the FFT
　　 4.7 Toeplitz and Related Systems
　　5 Orthogonalization and Least Squares
　　 5.1 Householder and Givens Matrices
　　 5.2 The QR Factorization
　　 5.3 The Full Rank LS Problem
　　 5.4 Other Orthogonal Factorizations
　　 5.5 The Rank Deficient LS Problem
　　 5.6 Weighting and Iterative Improvement
　　 5.7 Square and Underdetermined Systems
　　6 Parallel Matrix Computations
　　 6.1 Basic Concepts
　　 6.2 Matrix Multiplication
　　 6.3 Factorizations
　　4 Special Linear Systems
　　 4.1 The LDMw and LDLw Factorizations
　　 4.2 Positive Definite Systems
　　 4.3 Banded Systems
　　 4.4 Symmetric Indefinite Systems
　　 4.5 Block Systems
　　 4.6 Vandermonde Systems and the FFT
　　 4.7 Toeplitz and Related Systems
　　5 Orthogonalization and Least Squares
　　 5.1 Householder and Givens Matrices
　　 5.2 The QR Factorization
　　 5.3 The Full Rank LS Problem
　　 5.4 Other Orthogonal Factorizations
　　 5.5 The Rank Deficient LS Problem
　　 5.6 Weighting and Iterative Improvement
　　 5.7 Square and Underdetermined Systems
　　6 Parallel Matrix Computation
　　 6.1 Basic Concepts
　　 6.2 Matrix Multiplication
　　 6.3 Factorizations
　　7 The Unsymmetric Eigenvalue Problem
　　 7.1 Properties and Decompositions
　　 7.2 Perturbation Theory
　　 7.3 Power Iterations
　　 7.4 The Hessenberg and Real Schur Forms
　　 7.5 The Practical QR Algorithm
　　 7.6 Invariant Subspace Computations
　　 7.7 The QZ Method for Ax = A Bx
　　8 The Symmetric Eigenvalue Problem
　　 8.1 Properties and Decompositions
　　 8.2 Power Iterations
　　 8.3 The Symmetric QR Algorithm
　　 8.4 Jacobi Methods
　　 8.5 Tridiagonal Methods
　　 8.6 Computing the SVD
　　 8.7 Some Generalized Eigenvalue Problems
　　9 Lanczos Methods
　　 9.1 Derivation and Convergence Properties
　　 9.2 Practical Lanczos Procedures
　　 9.3 Applications to Ax = b and Least Squares
　　 9.4 Arnoldi and Unsymmetric Lanczos
　　10 Iterative Methods for Linear Systems
　　 10.1 The Standard Iterations 9
　　 10.2 The Conjugate Gradient Method
　　 10.3 Preconditioned Conjugate Gradients
　　 10.4 Other Krylov Subspace Methods
　　11 Functions of Matrices
　　 11.1 Eigenvalue Methods
　　 11.2 Approximation Methods
　　 11.3 The Matrix Exponential
　　12 Special Topics
　　 12.1 Constrained Least Squares
　　 12.2 Subset Selection Using the SVD
　　 12.3 Total Least Squares
　　 12.4 Computing Subspaces with the SVD
　　 12.5 Updating Matrix Factorizations
　　 12.6 Modified/Structured Eignproblems
　　Index