Numerical Linear Algebra
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-361-9 (ISBN)
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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.
Lloyd N. Trefethen is a Professor of Computer Science at Cornell University. Starting October 1, 1997, he will be the Professor of Numerical Analysis at Oxford University in England. He has won teaching awards at both MIT and Cornell. In addition to editorial positions on such journals as SIAM Journal on Numerical Analysis, Journal of Computational and Applied Mathematics, Numerische Mathematik, and SIAM Review, he has been an invited lecturer at two dozen international conferences. While at Cornell, David Bau was a student of Trefethen. He is currently a Software Engineer at Google Inc., where he helped develop Google Talk, Google's IM and VOIP service.
Preface
Acknowledgments
Part I: Fundamentals.
Lecture 1: Matrix-Vector Multiplication
Lecture 2: Orthogonal Vectors and Matrices
Lecture 3: Norms
Lecture 4: The Singular Value Decomposition
Lecture 5: More on the SVD
Part II: QR Factorization and Least Squares.
Lecture 6: Projectors
Lecture 7: QR Factorization
Lecture 8: Gram-Schmidt Orthogonalization
Lecture 9: MATLAB
Lecture 10: Householder Triangularization
Lecture 11: Least Squares Problems
Part III: Conditioning and Stability.
Lecture 12: Conditioning and Condition Numbers
Lecture 13: Floating Point Arithmetic
Lecture 14: Stability
Lecture 15: More on Stability
Lecture 16: Stability of Householder Triangularization
Lecture 17: Stability of Back Substitution
Lecture 18: Conditioning of Least Squares Problems
Lecture 19: Stability of Least Squares Algorithms
Part IV: Systems of Equations.
Lecture 20: Gaussian Elimination
Lecture 21: Pivoting
Lecture 22: Stability of Gaussian Elimination
Lecture 23: Cholesky Factorization
Part V: Eigenvalues.
Lecture 24: Eigenvalue Problems
Lecture 25: Overview of Eigenvalue Algorithms
Lecture 26: Reduction to Hessenberg or Tridiagonal Form
Lecture 27: Rayleigh Quotient, Inverse Iteration
Lecture 28: QR Algorithm without Shifts
Lecture 29: QR Algorithm with Shifts
Lecture 30: Other Eigenvalue Algorithms
Lecture 31: Computing the SVD
Part VI: Iterative Methods.
Lecture 32: Overview of Iterative Methods
Lecture 33: The Arnoldi Iteration
Lecture 34: How Arnoldi Locates Eigenvalues
Lecture 35: GMRES
Lecture 36: The Lanczos Iteration
Lecture 37: From Lanczos to Gauss Quadrature
Lecture 38: Conjugate Gradients
Lecture 39: Biorthogonalization Methods
Lecture 40: Preconditioning
Appendix: The Definition of Numerical Analysis
Notes
Bibliography
Index.
| Erscheint lt. Verlag | 30.6.1997 |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 177 x 256 mm |
| Gewicht | 673 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| ISBN-10 | 0-89871-361-7 / 0898713617 |
| ISBN-13 | 978-0-89871-361-9 / 9780898713619 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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