Chapter
Licensed
Unlicensed
Requires Authentication
9 Iterative regularization principle
You are currently not able to access this content.
You are currently not able to access this content.
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1 The regularity condition. Newton’s method 1
- 2 The Gauss–Newton method 10
- 3 The gradient method 16
- 4 Tikhonov’s scheme 23
- 5 Tikhonov’s scheme for linear equations 32
- 6 The gradient scheme for linear equations 45
- 7 Convergence rates for the approximation methods in the case of linear irregular equations 54
- 8 Equations with a convex discrepancy functional by Tikhonov’s method 64
- 9 Iterative regularization principle 69
- 10 The iteratively regularized Gauss–Newton method 76
- 11 The stable gradient method for irregular nonlinear equations 90
- 12 Relative computational efficiency of iteratively regularized methods 98
- 13 Numerical investigation of two-dimensional inverse gravimetry problem 103
- 14 Iteratively regularized methods for inverse problem in optical tomography 111
- 15 Feigenbaum’s universality equation 123
- 16 Conclusion 130
- References 132
- Index 137
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1 The regularity condition. Newton’s method 1
- 2 The Gauss–Newton method 10
- 3 The gradient method 16
- 4 Tikhonov’s scheme 23
- 5 Tikhonov’s scheme for linear equations 32
- 6 The gradient scheme for linear equations 45
- 7 Convergence rates for the approximation methods in the case of linear irregular equations 54
- 8 Equations with a convex discrepancy functional by Tikhonov’s method 64
- 9 Iterative regularization principle 69
- 10 The iteratively regularized Gauss–Newton method 76
- 11 The stable gradient method for irregular nonlinear equations 90
- 12 Relative computational efficiency of iteratively regularized methods 98
- 13 Numerical investigation of two-dimensional inverse gravimetry problem 103
- 14 Iteratively regularized methods for inverse problem in optical tomography 111
- 15 Feigenbaum’s universality equation 123
- 16 Conclusion 130
- References 132
- Index 137