Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will…mehr
Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions.
Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
Anatoly B. Bakushinsky, Institute of System Analysis,Russian Academy of Sciences, Moscow, Russia; Mihail Yu. Kokurin, Mari State Technical University, Yoshkar-Ola, Russia; Alexandra Smirnova, Georgia State University, Atlanta, Georgia, USA.
Inhaltsangabe
1 Regularity Condition. Newton's Method 2 The Gauss-Newton Method 3 The Gradient Method 4 Tikhonov's Scheme 5 Tikhonov's Scheme for Linear Equations 6 The Gradient Scheme for Linear Equations 7 Convergence Rates for the Approximation Methods in the Case of Linear Irregular Equations 8 Equations with a Convex Discrepancy Functional by Tikhonov's Method 9 Iterative Regularization Principle 10 The Iteratively Regularized Gauss-Newton Method 11 The Stable Gradient Method for Irregular Nonlinear Equations 12 Relative Computational Efficiency of Iteratively Regularized Methods 13 Numerical Investigation of Two-Dimensional Inverse Gravimetry Problem 14 Iteratively Regularized Methods for Inverse Problem in Optical Tomography 15 Feigenbaum's Universality Equation 16 Conclusion References Index
1 Regularity Condition. Newton's Method 2 The Gauss-Newton Method 3 The Gradient Method 4 Tikhonov's Scheme 5 Tikhonov's Scheme for Linear Equations 6 The Gradient Scheme for Linear Equations 7 Convergence Rates for the Approximation Methods in the Case of Linear Irregular Equations 8 Equations with a Convex Discrepancy Functional by Tikhonov's Method 9 Iterative Regularization Principle 10 The Iteratively Regularized Gauss-Newton Method 11 The Stable Gradient Method for Irregular Nonlinear Equations 12 Relative Computational Efficiency of Iteratively Regularized Methods 13 Numerical Investigation of Two-Dimensional Inverse Gravimetry Problem 14 Iteratively Regularized Methods for Inverse Problem in Optical Tomography 15 Feigenbaum's Universality Equation 16 Conclusion References Index
Rezensionen
"The book is an introduction to iterative methods for ill-posed problems. The style of writing is very user-friendly, in the best tradition of the Russian mathematical school. It is a valuable addition to the literature of ill-posed problems." Anton Suhadolc in: University of Michigan Mathematical Reviews 2012c
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