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Matrix Computations

ISBN-10: 1421407949
ISBN-13: 9781421407944
Edition: 4th 2013
List price: $74.00 Buy it from $38.57
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Description: The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution  More...

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Book details

List price: $74.00
Edition: 4th
Copyright year: 2013
Publisher: Johns Hopkins University Press
Publication date: 12/27/2012
Binding: Hardcover
Pages: 784
Size: 7.25" wide x 10.50" long x 2.00" tall
Weight: 4.136
Language: English

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this text useful and engaging. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

Preface
Global References
Other Books
Useful URLs
Common Notation
Matrix Multiplication
Basic Algorithms and Notation
Structure and Efficiency
Block Matrices and Algorithms
Fast Matrix-Vector Products
Vectorization and Locality
Parallel Matrix Multiplication
Matrix Analysis
Basic Ideas from Linear Algebra
Vector Norms
Matrix Norms
The Singular Value Decomposition
Subspace Metrics
The Sensitivity of Square Systems
Finite Precision Matrix Computations
General Linear Systems
Triangular Systems
The LU Factorization
Round off Error in Gaussian Elimination
Pivoting
Improving and Estimating Accuracy
Parallel LU
Special Linear Systems
Diagonal Dominance and Symmetry
Positive Definite Systems
Banded Systems
Symmetric Indefinite Systems
Block Tridiagonal Systems
Vandermonde Systems
Classical Methods for Toeplitz Systems
Circulant and Discrete Poisson Systems
Orthogonalization and Least Squares
Householder and Givens Transformations
The QR Factorization
The Full-Rank Least Squares Problem
Other Orthogonal Factorizations
The Rank-Deficient Least Squares Problem
Square and Underdetermined Systems
Modified Least Squares Problems and Methods
Weighting and Regularization
Constrained Least Squares
Total Least Squares
Subspace Computations with the SVD
Updating Matrix Factorizations
Unsymmetric Eigenvalue Problems
Properties and Decompositions
Perturbation Theory
Power Iterations
The Hessenberg and Real Schur Forms
The Practical QR Algorithm
Invariant Subspace Computations
The Generalized Eigenvalue Problem
Hamiltonian and Product Eigenvalue Problems
Pseudospectra
Symmetric Eigenvalue Problems
Properties and Decompositions
Power Iterations
The Symmetric QR Algorithm
More Methods for Tridiagonal Problems
Jacobi Methods
Computing the SVD
Generalized Eigenvalue Problems with Symmetry
Functions of Matrices
Eigenvalue Methods
Approximation Methods
The Matrix Exponential
The Sign, Square Root, and Log of a Matrix
Large Sparse Eigenvalue Problems
The Symmetric Lanczos Process
Lanczos, Quadrature, and Approximation
Practical Lanczos Procedures
Large Sparse SVD Frameworks
Krylov Methods for Unsymmetric Problems
Jacobi-Davidson and Related Methods
Large Sparse Linear System Problems
Direct Methods
The Classical Iterations
The Conjugate Gradient Method
Other Krylov Methods
Preconditioning
The Multigrid Framework
Special Topics
Linear Systems with Displacement Structure
Structured-Rank Problems
Kronecker Product Computations
Tensor Unfoldings and Contractions
Tensor Decompositions and Iterations
Index

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