Numerical Linear Algebra

Front Cover
SIAM, Jun 1, 1997 - Mathematics - 361 pages
9 Reviews
This is a concise, insightful introduction to the field of numerical linear algebra. The clarity and eloquence of the presentation make it popular with teachers and students alike. The text aims to expand the reader's view of the field and to present standard material in a novel way. All of the most important topics in the field are covered with a fresh perspective, including iterative methods for systems of equations and eigenvalue problems and the underlying principles of conditioning and stability. Presentation is in the form of 40 lectures, which each focus on one or two central ideas. The unity between topics is emphasized throughout, with no risk of getting lost in details and technicalities. The book breaks with tradition by beginning with the QR factorization - an important and fresh idea for students, and the thread that connects most of the algorithms of numerical linear algebra.
  

What people are saying - Write a review

User ratings

5 stars
3
4 stars
4
3 stars
1
2 stars
1
1 star
0

User Review - Flag as inappropriate

This is an excellent book on numerical linear algebra, a very good textbook for a senior undergraduate course. I like the writing style and have been enjoying the reading. Very often it explains "why", not just gives "what" and "how". Highly recommended.

User Review - Flag as inappropriate

The strength of this book is in the conceptual discussions. This isn't the book to use to learn the mechanics of the methods described. It's one of my three favorite numerical linear algebra books.

Contents

Fundamentals
8
MatrixVector Multiplication
9
Orthogonal Vectors and Matrices
11
Norms
17
The Singular Value Decomposition
25
More on the SVD
32
QR Factorization and Least Squares
39
Projectors
41
Cholesky Factorization
172
Eigenvalues
179
Eigenvalue Problems
181
Overview of Eigenvalue Algorithms
190
Reduction to Hessenberg or Tridiagonal Form
196
Rayleigh Quotient Inverse Iteration
202
QR Algorithm without Shifts
211
QR Algorithm with Shifts
219

QR Factorization
48
Gram Schmidt Orthogonalization
56
MATLAB
63
Householder Triangularization
69
Least Squares Problems
77
Conditioning and Stability
87
Conditioning and Condition Numbers
89
Floating Point Arithmetic
97
Stability
102
More on Stability
108
Stability of Householder Triangularization
114
Stability of Back Substitution
121
Conditioning of Least Squares Problems
129
Stability of Least Squares Algorithms
137
Systems of Equations
145
Gaussian Elimination
147
Pivoting
155
Stability of Gaussian Elimination
163
Other Eigenvalue Algorithms
225
Computing the SVD
234
Iterative Methods
241
Overview of Iterative Methods
243
The Arnoldi Iteration
250
How Arnoldi Locates Eigenvalues
257
GMRES
266
The Lanczos Iteration
276
From Lanczos to Gauss Quadrature
285
Conjugate Gradients
293
Biorthogonalization Methods
303
Preconditioning
313
Appendix The Definition of Numerical Analysis
321
Notes
329
Bibliography
343
Index
353
Copyright

Common terms and phrases

References to this book

All Book Search results »

About the author (1997)

Nick Trefethen is Professor of Numerical Analysis at the University of Oxford and a Fellow of the Royal Society. During 2011 12 he served as President of SIAM.

David Bau is a computer scientist who develops image search algorithms for Google. He is a father of three, and he loves sharing his passion for programming with kids.

Bibliographic information