8. Automatic differentiation

Chapters in this book

1. Frontmatter i
2. Preface vii
3. Contents xi
4. 1. Preliminaries 1
5. 2. Real intervals 75
6. 3. Interval vectors, interval matrices 109
7. 4. Expressions, P-contraction, ε-inflation 125
8. 5. Linear systems of equations 159
9. 6. Nonlinear systems of equations 289
10. 7. Eigenvalue problems and related ones 345
11. 8. Automatic differentiation 407
12. 9. Complex intervals 417
13. Final Remarks 433
14. Appendix
15. A. Proof of the Jordan normal form 437
16. B. Two elementary proofs of Brouwer’s fixed point theorem 439
17. C. Proof of the Newton–Kantorovich Theorem 445
18. D. Convergence proof of the row cyclic Jacobi method 451
19. E. The CORDIC algorithm 457
20. F. The symmetric solution set – a proof of Theorem 5.2.6 463
21. G. A short introduction to INTLAB 469
22. Bibliography 483
23. Symbol Index 499
24. Author Index 505
25. Subject Index 509