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Schwartz , Linear Operators. General Theory. Interscience Publishers Efron , T. Hastie , I. Johnstone and R. Tibshirani , Least angle regression. Ekeland and R. Temam , Convex analysis and variational problems. North-Holland Engl and G. Landl , Convergence rates for maximum entropy regularization.
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Neubauer , Regularization of Inverse Problems. Kluwer Academic Publishers Figueiredo , R. Nowak and S. Wright , Gradient projection for sparse reconstruction : Application to compressed sensing and other inverse problems. IEEE J. Signal Process. Fonseca and G. Leoni , Modern methods in the calculus of variations : Lp spaces. Fornasier and H.
Rauhut , Recovery algorithms for vector valued data with joint sparsity constraints. The first part deals with convergence rates theory for Tikhonov regularization as classical regularization method. In particular, generalizations of well-established results in Hilbert spaces are presented in the Banach space situation.
Since the numerical effort of Tikhonov regularization in applications is rather high iterative approaches were considered as alternative regularization variants in the second part. In particular, two Gradient-type methods were presented and their behaviour concerning convergence and stability is investigated. Return to Book Page.
gatsbyroofs.co.uk/map61.php Barbara Kaltenbacher. Bernd Hofmann. Kamil S Kazimierski. 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 diffe Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems.
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 V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels. Get A Copy. Published July 30th by de Gruyter first published July 1st