03496nam a2200517 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001200139100002100151245014500172260004300317300001100360653002800371653002200399653002100421653002600442653003600468653003600504653002800540653001800568653006200586653002600648653006600674653002500740653001700765700002900782700003600811700003600847041001900883989003800902490005800940500004800998028002601046773005801072773005701130773006001187773004701247773003301294773005701327856008701384082001301471520149401484EB000350233EBX0100000000000000020151200000000000000.0tu|||||||||||||||||||||130408 r ||| eng a9783110255720 4aQA322.21 aSchuster, Thomas00aRegularization Methods in Banach SpaceshElektronische RessourcecBernd Hofmann, Barbara Kaltenbacher, Kamil S. Kazimierski, Thomas Schuster aBerlinbDe Gruyterc[2012]©2012, 2012 a294 p. aTikhonov regularization aIterative methods aIterative Method aRegularization theory aMATHEMATICS / Applied / bisacsh aDifferential equations, Partial aTikhonov Regularization aBanach spaces a(DE-601)104603658 / (DE-588)4004402-6 / Banach-Raum / gnd aRegularization Theory a(DE-601)105750670 / (DE-588)4124043-1 / Regularisierung / gnd aParameter estimation aBanach Space1 aHofmann, Bernde[author]1 aKaltenbacher, Barbarae[author]1 aKazimierski, Kamil S.e[author]07aeng2ISO 639-2 bGRUYMPGaDeGruyter MPG Collection0 aRadon Series on Computational and Applied Mathematics aMode of access: Internet via World Wide Web50a10.1515/97831102557200 tE-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 20120 tDGBA Backlist Mathematics English Language 2000-20140 tDGBA Backlist Complete English Language 2000-2014 PART10 tE-BOOK GESAMTPAKET / COMPLETE PACKAGE 20120 tDGBA Mathematics 2000 - 20140 tE-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 201240uhttps://www.degruyter.com/doi/book/10.1515/9783110255720?nosfx=yxVerlag3Volltext0 a515 .732 aRegularization 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