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Numerical linear algebra /
Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all field...
| Cote: | Libro Electrónico |
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| Format: | Livre |
| Langue: | Inglés |
| Publié: |
Philadelphia, Pa. :
Society for Industrial and Applied Mathematics,
1997.
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| Sujets: | |
| Accès en ligne: | Description Description *** |
Table des matières:
- Preface; Acknowledgments; Part I: Fundamentals. 1. Matrix-Vector Multiplication; 2. Orthogonal Vectors and Matrices; 3. Norms; 4. The Singular Value Decomposition; 5. More on the SVD; Part II: QR Factorization and Least Squares. 6. Projectors; 7. QR Factorization; 1. Gram-Schmidt Orthogonalization; 1. MATLAB; 10. Householder Triangularization; 11. Least Squares Problems; Part III: Conditioning and Stability. 12. Conditioning and Condition Numbers; 13. Floating Point Arithmetic; 14. Stability; 15. More on Stability; 16. Stability of Householder Triangularization; 17. Stability of Back Substitution; 18. Conditioning of Least Squares Problems; 19. Stability of Least Squares Algorithms;
- Part IV: Systems of Equations. 20. Taussian Elimination; 21. Pivoting; 22. Stability of Gaussian Elimination; 23. Cholesky Factorization; Part V: Eigenvalues. 24. Eigenvalue Problems; 25. Overview of Eigenvalue Algorithms; 26. Reduction to Hessenberg or Tridiagonal Form; 27. Rayleigh Quotient, Inverse Iteration; 28. QR Algorithm without Shifts; 29. QR Algorithm with Shifts; Lecture 30. Other Eigenvalue Algorithms; Lecture 31. Computing the SVD; Part VI: Iterative Methods. 32. Overview of Iterative Methods; 33. The Arnoldi Iteration; 34. How Arnoldi Locates Eigenvalues; 35. GMRES; 36. The Lanczos Iteration; 37. From Lanczos to Gauss Quadrature; 38. Conjugate Gradients; 39. Biorthogonalization Methods; 40. Preconditioning; Appendix : The Definition of Numerical Analysis; Notes; Bibliography; Index.