ISBN: 9780792361312
ID: 6387079
Iteration regularization, i.e, utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari- zation algorithms is developed, which allows us to consider linear. Iteration regularization, i.e, utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari- zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the 'classical' iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given. Books, Science and Geography~~Mathematics~~Calculus & Mathematical Analysis, Regularization Of Ill-Posed Problems By Iteration Methods~~Book~~9780792361312~~S.F. Gilyazov, N.L. Goldman, , , , , , , , , ,, [PU: Kluwer Academic Publishers]
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S. F. Gilyazov#Nataliya Gol'dman:
Regularization of Ill-Posed Problems by Iteration Methods - new bookISBN: 9780792361312
ID: b7b6835c38a0da834dd7c59113e48120
Regularization of Ill-Posed Problems by Iteration Methods Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the 'classical' iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given. Bücher / Fremdsprachige Bücher / Englische Bücher 978-0-7923-6131-2, Springer
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ISBN: 9780792361312
ID: 499584095
Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the ´classical´ iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given. Regularization of Ill-Posed Problems by Iteration Methods Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer
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ISBN: 9780792361312
ID: 978079236131
This volume presents new results in regularization of ill-posed problems by iteration methods, which is one of the most important and rapidly developing topics of the theory of ill-posed problems. The new theoretical results are connected with the proposed united approach to the proof of regularizing properties of the `classical'' iteration methods (steepest descent, conjugate direction) complemented by the stopping rule depending on the level of errors in the input data. Much emphasis is given to the choice of the iteration index as the regularization parameter and to the rate convergence estimates of the approximate solutions. Results of calculations for important applications in non-linear thermophysics are also presented. Audience: This work will be a useful resource for specialists in the theory of partial differential and integral equations, in numerical analysis and in theory and methods. S.F. Gilyazov, Nataliya Gol'dman, Books, Science and Nature, Regularization of Ill-Posed Problems by Iteration Methods Books>Science and Nature, Springer Netherlands
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ISBN: 9780792361312
ID: 9780792361312
Regularization of Ill-Posed Problems by Iteration Methods Regularization-of-Ill-posed-Problems-by-Iteration-Methods~~S-F-Gilyazov Science/Tech>Mathematics>Mathematics Hardcover, Springer Netherlands
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Title: | Regularization of Ill-Posed Problems by Iteration Methods |
ISBN: | 0792361318 |
Details of the book - Regularization of Ill-Posed Problems by Iteration Methods
EAN (ISBN-13): 9780792361312
ISBN (ISBN-10): 0792361318
Hardcover
Publishing year: 1999
Publisher: Springer-Verlag GmbH
356 Pages
Weight: 0,695 kg
Language: eng/Englisch
Book in our database since 29.03.2007 04:25:17
Book found last time on 22.05.2016 19:29:33
ISBN/EAN: 0792361318
ISBN - alternate spelling:
0-7923-6131-8, 978-0-7923-6131-2
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