Regularization Methods in Banach Spaces: 10 - Rilegato

Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S.

Rilegato

ISBN 10: 3110255243 ISBN 13: 9783110255249

Casa editrice: De Gruyter, 2012

Riassunto

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods.

This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Su questo libro

Informazioni sull?autore

Thomas Schuster, Carl von Ossietzky Universität Oldenburg, Germany; Barbara Kaltenbacher, University of Stuttgart, Germany; Bernd Hofmann, Chemnitz University of Technology, Germany; Kamil S. Kazimierski, University of Bremen, Germany.

Dalla quarta di copertina

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods.

This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Dettagli dell'edizione

• Editore: De Gruyter
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3110255243
• ISBN 13: 9783110255249
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 283
• Contatto del produttore: non disponibile
• Persona responsabile: K. G. Saur; productsafety@degruyterbrill.com; ; Genthiner Straße 13; Berlin; 10785; Germania