Matrix Computations

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JHU Press, 2013 - Mathematics - 756 pages
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A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice.

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 book to be an indispensible tool.

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. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.


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algorithm to slove [U][L][X]=[B] Factorization


1 Matrix Multiplication
2 Matrix Analysis
3 General Linear Systems
4 Special Linear Systems
5 Orthogonalization and Least Squares
6 Modified Least Squares Problems and Methods
7 Unsymmetric Eigenvalue Problems
8 Symmetric Eigenvalue Problems
9 Functions of Matrices
10 Large Sparse Eigenvalue Problems
11 Large Sparse Linear System Problems
12 Special Topics

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About the author (2013)

Gene H. Golub (1932–2007) was a professor emeritus and former director of scientific computing and computational mathematics at Stanford University. Charles F. Van Loan is a professor of computer science at Cornell University, where he is the Joseph C. Ford Professor of Engineering.

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