Matrix Computations

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JHU Press, 2013 - Mathematics - 756 pages
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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.

 

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

Contents

1 Matrix Multiplication
1
2 Matrix Analysis
63
3 General Linear Systems
105
4 Special Linear Systems
153
5 Orthogonalization and Least Squares
233
6 Modified Least Squares Problems and Methods
303
7 Unsymmetric Eigenvalue Problems
347
8 Symmetric Eigenvalue Problems
439
9 Functions of Matrices
513
10 Large Sparse Eigenvalue Problems
545
11 Large Sparse Linear System Problems
597
12 Special Topics
681
Index
747
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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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