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• 2010038154 alternative "Iterativnye metody reshenii︠a︡ nekorrektnykh zadach. English".
• 2010038154 contributor B11782431.
• 2010038154 contributor B11782432.
• 2010038154 created "c2011.".
• 2010038154 date "2011".
• 2010038154 date "c2011.".
• 2010038154 dateCopyrighted "c2011.".
• 2010038154 description "12.3. Comparison to iteratively regularized gradient scheme -- Problems -- 13. Numerical investigation of two-dimensional inverse gravimetry problem -- 13.1. Problem formulation -- 13.2. The algorithm -- 13.3. Simulations -- Problems -- 14. Iteratively regularized methods for inverse problem in optical tomography -- 14.1. Statement of the problem -- 14.2. Simple example -- 14.3. Forward simulation -- 14.4. The inverse problem -- 14.5. Numerical results -- Problems -- 15. Feigenbaum's universality equation -- 15.1. The universal constants -- 15.2. Ill-posedness -- 15.3. Numerical algorithm for 2 ≤ z ≤ 12 -- 15.4. Regularized method for z ≥ 13 -- Problems -- 16. Conclusion.".
• 2010038154 description "5.4. A priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides -- 5.5. The discrepancy principle -- 5.6. Approximation of a quasi-solution -- Problems -- 6. The gradient scheme for linear equations -- 6.1. The technique of spectral analysis -- 6.2. A priori stopping rule -- 6.3. A posteriori stopping rule -- Problems -- 7. Convergence rates for the approximation methods in the case of linear irregular equations -- 7.1. The source-type condition (STC) -- 7.2. STC for the gradient method -- 7.3. The saturation phenomena -- 7.4. Approximations in case of a perturbed STC -- 7.5. Accuracy of the estimates -- Problems -- 8. Equations with a convex discrepancy functional by Tikhonov's method -- 8.1. Some difficulties associated with Tikhonov's method in case of a convex discrepancy functional".
• 2010038154 description "8.2. An illustrative example -- Problems -- 9. Iterative regularization principle -- 9.1. The idea of iterative regularization -- 9.2. The iteratively regularized gradient method -- Problems -- 10. The iteratively regularized Gauss -- Newton method -- 10.1. Convergence analysis -- 10.2. Further properties of IRGN iterations -- 10.3. A unified approach to the construction of iterative methods for irregular equations -- 10.4. The reverse connection control -- Problems -- 11. The stable gradient method for irregular nonlinear equations -- 11.1. Solving an auxiliary finite dimensional problem by the gradient descent method -- 11.2. Investigation of a difference inequality -- 11.3. The case of noisy data -- Problems -- 12. Relative computational efficiency of iteratively regularized methods -- 12.1. Generalized Gauss -- Newton methods -- 12.2. A more restrictive source condition".
• 2010038154 description "Includes bibliographical references and index.".
• 2010038154 description "Machine generated contents note: 1. The regularity condition. Newton's method -- 1.1. Preliminary results -- 1.2. Linearization procedure -- 1.3. Error analysis -- Problems -- 2. The Gauss -- Newton method -- 2.1. Motivation -- 2.2. Convergence rates -- Problems -- 3. The gradient method -- 3.1. The gradient method for regular problems -- 3.2. Ill-posed case -- Problems -- 4. Tikhonov's scheme -- 4.1. The Tikhonov functional -- 4.2. Properties of a minimizing sequence -- 4.3. Other types of convergence -- 4.4. Equations with noisy data -- Problems -- 5. Tikhonov's scheme for linear equations -- 5.1. The main convergence result -- 5.2. Elements of spectral theory -- 5.3. Minimizing sequences for linear equations".
• 2010038154 extent "xi, 136 p. :".
• 2010038154 format "text/html".
• 2010038154 identifier "3110250640 (alk. paper)".
• 2010038154 identifier "9783110250640 (alk. paper)".
• 2010038154 identifier 04.
• 2010038154 identifier dokserv?id=3645007&prov=M&dok_var=1&dok_ext=htm.
• 2010038154 isPartOf "Inverse and ill-posed problems series ; 54".
• 2010038154 isPartOf "Inverse and ill-posed problems series ; v. 54.".
• 2010038154 issued "2011".
• 2010038154 issued "c2011.".
• 2010038154 language "eng rus".
• 2010038154 language "eng".
• 2010038154 publisher "Berlin ; New York : De Gruyter,".
• 2010038154 subject "515/.353 22".
• 2010038154 subject "Differential equations, Partial Improperly posed problems.".
• 2010038154 subject "Iterative methods (Mathematics)".
• 2010038154 subject "QA377 .B25513 2011".
• 2010038154 tableOfContents "12.3. Comparison to iteratively regularized gradient scheme -- Problems -- 13. Numerical investigation of two-dimensional inverse gravimetry problem -- 13.1. Problem formulation -- 13.2. The algorithm -- 13.3. Simulations -- Problems -- 14. Iteratively regularized methods for inverse problem in optical tomography -- 14.1. Statement of the problem -- 14.2. Simple example -- 14.3. Forward simulation -- 14.4. The inverse problem -- 14.5. Numerical results -- Problems -- 15. Feigenbaum's universality equation -- 15.1. The universal constants -- 15.2. Ill-posedness -- 15.3. Numerical algorithm for 2 ≤ z ≤ 12 -- 15.4. Regularized method for z ≥ 13 -- Problems -- 16. Conclusion.".
• 2010038154 tableOfContents "5.4. A priori agreement between the regularization parameter and the error for equations with perturbed right-hand sides -- 5.5. The discrepancy principle -- 5.6. Approximation of a quasi-solution -- Problems -- 6. The gradient scheme for linear equations -- 6.1. The technique of spectral analysis -- 6.2. A priori stopping rule -- 6.3. A posteriori stopping rule -- Problems -- 7. Convergence rates for the approximation methods in the case of linear irregular equations -- 7.1. The source-type condition (STC) -- 7.2. STC for the gradient method -- 7.3. The saturation phenomena -- 7.4. Approximations in case of a perturbed STC -- 7.5. Accuracy of the estimates -- Problems -- 8. Equations with a convex discrepancy functional by Tikhonov's method -- 8.1. Some difficulties associated with Tikhonov's method in case of a convex discrepancy functional".
• 2010038154 tableOfContents "8.2. An illustrative example -- Problems -- 9. Iterative regularization principle -- 9.1. The idea of iterative regularization -- 9.2. The iteratively regularized gradient method -- Problems -- 10. The iteratively regularized Gauss -- Newton method -- 10.1. Convergence analysis -- 10.2. Further properties of IRGN iterations -- 10.3. A unified approach to the construction of iterative methods for irregular equations -- 10.4. The reverse connection control -- Problems -- 11. The stable gradient method for irregular nonlinear equations -- 11.1. Solving an auxiliary finite dimensional problem by the gradient descent method -- 11.2. Investigation of a difference inequality -- 11.3. The case of noisy data -- Problems -- 12. Relative computational efficiency of iteratively regularized methods -- 12.1. Generalized Gauss -- Newton methods -- 12.2. A more restrictive source condition".
• 2010038154 tableOfContents "Machine generated contents note: 1. The regularity condition. Newton's method -- 1.1. Preliminary results -- 1.2. Linearization procedure -- 1.3. Error analysis -- Problems -- 2. The Gauss -- Newton method -- 2.1. Motivation -- 2.2. Convergence rates -- Problems -- 3. The gradient method -- 3.1. The gradient method for regular problems -- 3.2. Ill-posed case -- Problems -- 4. Tikhonov's scheme -- 4.1. The Tikhonov functional -- 4.2. Properties of a minimizing sequence -- 4.3. Other types of convergence -- 4.4. Equations with noisy data -- Problems -- 5. Tikhonov's scheme for linear equations -- 5.1. The main convergence result -- 5.2. Elements of spectral theory -- 5.3. Minimizing sequences for linear equations".
• 2010038154 title "Iterative methods for ill-posed problems : an introduction / Anatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova.".
• 2010038154 title "Iterativnye metody reshenii︠a︡ nekorrektnykh zadach. English".
• 2010038154 type "text".