LEADER 04232nam 2200781 a 450 001 9910785935603321 005 20230801225154.0 010 $a3-11-025572-3 010 $a1-283-62792-2 010 $a9786613940377 024 7 $a10.1515/9783110255720 035 $a(CKB)2670000000274148 035 $a(EBL)893636 035 $a(OCoLC)812251485 035 $a(SSID)ssj0001054263 035 $a(PQKBManifestationID)11613277 035 $a(PQKBTitleCode)TC0001054263 035 $a(PQKBWorkID)11126835 035 $a(PQKB)10302289 035 $a(MiAaPQ)EBC893636 035 $a(DE-B1597)123677 035 $a(OCoLC)840446583 035 $a(DE-B1597)9783110255720 035 $a(Au-PeEL)EBL893636 035 $a(CaPaEBR)ebr10606482 035 $a(CaONFJC)MIL394037 035 $a(EXLCZ)992670000000274148 100 $a20120405d2012 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aRegularization methods in Banach spaces$b[electronic resource] /$fby Thomas Schuster ... [et al.] 210 $aBerlin ;$aBoston $cDe Gruyter$dc2012 215 $a1 online resource (296 p.) 225 0 $aRadon series on computational and applied mathematics,$x1865-3707 ;$v10 225 0 $aRadon Series on Computational and Applied Mathematics ;$v10 300 $aDescription based upon print version of record. 311 0 $a3-11-220450-6 311 0 $a3-11-025524-3 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tPart I. Why to use Banach spaces in regularization theory? --$tPart II. Geometry and mathematical tools of Banach spaces --$tPart III. Tikhonov-type regularization --$tPart IV. Iterative regularization --$tPart V. The method of approximate inverse --$tBibliography --$tIndex 330 $aRegularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels. 410 0$aRadon Series on Computational and Applied Mathematics 606 $aBanach spaces 606 $aParameter estimation 606 $aDifferential equations, Partial 610 $aBanach Space. 610 $aIterative Method. 610 $aRegularization Theory. 610 $aTikhonov Regularization. 615 0$aBanach spaces. 615 0$aParameter estimation. 615 0$aDifferential equations, Partial. 676 $a515/.732 686 $aSK 520$qSEPA$2rvk 700 $aSchuster$b Thomas$f1971-$01162550 702 $aHofmann$b Bernd 702 $aKaltenbacher$b Barbara 702 $aKazimierski$b Kamil S. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910785935603321 996 $aRegularization methods in Banach spaces$93718160 997 $aUNINA