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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Trefethen, Lloyd Nicholas
Corporate Author: Society for Industrial and Applied Mathematics
Other Authors: Bau, David
Format: Book
Language:Inglés
Published: Philadelphia, Pa. : Society for Industrial and Applied Mathematics, 1997.
Subjects:
Álgebra lineal
Numerical calculations.
Algebra lineal.
Cálculo numérico
Online Access:Description
Description ***
Table of Contents:
  • 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.

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