3 The gradient method

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents IX
4. 1 The regularity condition. Newton’s method 1
5. 2 The Gauss–Newton method 10
6. 3 The gradient method 16
7. 4 Tikhonov’s scheme 23
8. 5 Tikhonov’s scheme for linear equations 32
9. 6 The gradient scheme for linear equations 45
10. 7 Convergence rates for the approximation methods in the case of linear irregular equations 54
11. 8 Equations with a convex discrepancy functional by Tikhonov’s method 64
12. 9 Iterative regularization principle 69
13. 10 The iteratively regularized Gauss–Newton method 76
14. 11 The stable gradient method for irregular nonlinear equations 90
15. 12 Relative computational efficiency of iteratively regularized methods 98
16. 13 Numerical investigation of two-dimensional inverse gravimetry problem 103
17. 14 Iteratively regularized methods for inverse problem in optical tomography 111
18. 15 Feigenbaum’s universality equation 123
19. 16 Conclusion 130
20. References 132
21. Index 137