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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Regularization of Ill-Posed Problems by Iteration Methods
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Regularization of Ill-Posed Problems by Iteration Methods
S.F. Gilyazov, N.L. Gol'dman (Broschiert, Englisch)
Optischer Zustand
Beschreibung
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. 53,49 €
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Technische Daten
Erscheinungsdatum
09.12.2010
Sprache
Englisch
EAN
9789048153824
Herausgeber
Springer Netherland
Serien- oder Bandtitel
Mathematics and Its Applications
Sonderedition
Nein
Autor
S.F. Gilyazov, N.L. Gol'dman
Seitenanzahl
342
Einbandart
Broschiert
Schlagwörter
Calc, Calculation, DEX, Integral equation, Volume, algorithms, convergence, equation, integral, iteration, numerical analysis, online, operator, proof, partial differential equations
Thema-Inhalt
PBKS - Numerische Mathematik
PBKF - Funktionalanalysis und Abwandlungen
PBKJ - Differentialrechnung und -gleichungen
PBKL - Integralrechnung und -gleichungen
TRC - Fahrzeugbau
Höhe
240 mm
Breite
16 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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