TY  - BOOK
AU  - BakushinskiÄ­,A.B.
AU  - Kokurin,M.I︠U︡
AU  - Smirnova,A.B.
TI  - Iterative methods for ill-posed problems: an introduction 
T2  - Inverse and ill-posed problems series
SN  - 9783110250640
AV  - QA377 B166 I 2011
PY  - 2011///
CY  - Berlin, New York
PB  - De Gruyter
KW  - Differential equations, Partial
KW  - Improperly posed problems
KW  - Iterative methods (Mathematics)
N1  - The regularity condition. Newton's method --; Preliminary results --; Linearization procedure --; Error analysis --; Problems --; The Gauss -- Newton method --; Motivation --; Convergence rates --; Problems --; The gradient method --; The gradient method for regular problems --; Ill-posed case --; Problems --; Tikhonov's scheme --; The Tikhonov functional --; Properties of a minimizing sequence --; Other types of convergence --; Equations with noisy data --; Problems --; Tikhonov's scheme for linear equations --; The main convergence result --; Elements of spectral theory --; Minimizing sequences for linear equations; A priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides --; The discrepancy principle --; Approximation of a quasi-solution --; Problems --; The gradient scheme for linear equations --; The technique of spectral analysis --; A priori stopping rule --; A posteriori stopping rule --; Problems --; Convergence rates for the approximation methods in the case of linear irregular equations --; The source-type condition (STC) --; STC for the gradient method --; The saturation phenomena --; Approximations in case of a perturbed STC --; Accuracy of the estimates --; Problems --; Equations with a convex discrepancy functional by Tikhonov's method --; Some difficulties associated with Tikhonov's method in case of a convex discrepancy functional; An illustrative example --; Problems --; Iterative regularization principle --; The idea of iterative regularization --; The iteratively regularized gradient method --; Problems --; The iteratively regularized Gauss -- Newton method --; Convergence analysis --; Further properties of IRGN iterations --; A unified approach to the construction of iterative methods for irregular equations --; The reverse connection control --; Problems --; The stable gradient method for irregular nonlinear equations --; Solving an auxiliary finite dimensional problem by the gradient descent method --; Investigation of a difference inequality --; The case of noisy data --; Problems --; Relative computational efficiency of iteratively regularized methods --; Generalized Gauss -- Newton methods --; A more restrictive source condition; Comparison to iteratively regularized gradient scheme --; Problems --; Numerical investigation of two-dimensional inverse gravimetry problem --; Problem formulation --; The algorithm --; Simulations --; Problems --; Iteratively regularized methods for inverse problem in optical tomography --; Statement of the problem --; Simple example --; Forward simulation --; The inverse problem --; Numerical results --; Problems --; Feigenbaum's universality equation --; The universal constants --; Ill-posedness --; Numerical algorithm for 2 ≤ z ≤ 12 --; Regularized method for z ≥ 13 --; Problems --; Conclusion; HKBU library; YT2025 M10
ER  -