Beautiful! Very simply, if you want to have an insight on linear algebraic procedures, and why this and that happens so and so, this is the book. Topic-wise, it is almost complete for a first treatment. Each chapter starts with a gentle introduction, building intuition and then gets into the formal material. The style is solid.
Although talking about procedures, it also attempts to give some geometric intuition here and there. It helps.
This is not a reference book though. You cannot find every important procedure.
Author(s): Lloyd N. Trefethen, David Bau III
Publisher: Society for Industrial and Applied Mathematics
Year: 1997
Language: English
Pages: 375
City: Philadelphia
Tags: Математика;Вычислительная математика;Вычислительные методы линейной алгебры;
NUMERICAL LINEAR ALGEBRA......Page 1
Contents......Page 9
Preface......Page 11
Acknowledgments......Page 13
Part I Fundament als......Page 15
Lecture 1. Matrix-Vector Multiplication......Page 17
Lecture 2. Orthogonal Vectors and Matrices......Page 25
Lecture 3. Norms......Page 31
Lecture 4. The Singular Value Decomposition......Page 39
Lecture 5. More on the SVD......Page 46
Part II QR Factorization and Least Squares......Page 53
Lecture 6. Projectors......Page 55
Lecture 7. QR Factorization......Page 62
Lecture 8. Gram-Schmidt Orthogonalization......Page 70
Lecture 9. MATLAB......Page 77
Lecture 10. Householder Triangularization......Page 83
Lecture 11. Least Squares Problems......Page 91
Part III Conditioning and Stability......Page 101
Lecture 12. Conditioning and Condition Numbers......Page 103
Lecture 13. Floating Point Arithmetic......Page 111
Lecture 14. Stability......Page 116
Lecture 15. More on Stability......Page 122
Lecture 16. Stability of Householder Triangularization......Page 128
Lecture 17. Stability of Back Substitution......Page 135
Lecture 18. Conditioning of Least Squares Problems......Page 143
Lecture 19. Stability of Least Squares Algorithms......Page 151
Part IV Systems of Equations......Page 159
Lecture 20. Gaussian Elimination......Page 161
Lecture 21. Pivoting......Page 169
Lecture 22. Stability of Gaussian Elimination......Page 177
Lecture 23. Cholesky Factorization......Page 186
Part V Eigenvalues......Page 193
Lecture 24. Eigenvalue Problems......Page 195
Lecture 25. Overview of Eigenvalue Algorithms......Page 204
Lecture 26. Reduction to Hessenberg or Tridiagonal Form......Page 210
Lecture 27. Rayleigh Quotient, Inverse Iteration......Page 216
Lecture 28. QR Algorithm without Shifts......Page 225
Lecture 30. Other Eigenvalue Algorithms......Page 239
Lecture 31. Computing the SVD......Page 248
Part VI Iterative Methods......Page 255
Lecture 32. Overview of Iterative Methods......Page 257
Lecture 33. The Arnold! Iteration......Page 264
Lecture 34. How Arnold! Locates Eigenvalues......Page 271
Lecture 35. GMRES......Page 280
Lecture 36. The Lanczos Iteration......Page 290
Lecture 37. From Lanczos to Gauss Quadrature......Page 299
Lecture 38. Conjugate Gradients......Page 307
Lecture 39. Biorthogonalization Methods......Page 317
Lecture 40. Preconditioning......Page 327
Appendix. The Definition of Numerical Analysis......Page 335
Notes......Page 343
Bibliography......Page 357
Index......Page 367
