Scientific Publications of Andreas Neubauer


Books


(with M. Burger and B. Kaltenbacher), Iterative Solution Methods, in: S. Scherzer, ed., Handbook of Mathematical Methods in Imaging, Springer, Berlin, Heidelberg, New York, 2011, 345-384.


(with B. Kaltenbacher and O. Scherzer), Iterative Regularization Methods for Nonlinear Ill-Posed Problems, Radon Series on Computational and Applied Mathematics, de Gruyter, Berlin, 2008.


(with H.W. Engl and M. Hanke), Regularization of Inverse Problems, Kluwer, Dordrecht, 1996.



Papers


(with S. Hubmer, E. Sherina, A. Neubauer, and O. Scherzer ), Lame parameter estimation from static displacement field measurements in the framework of nonlinear inverse problems, SIAM J. Imaging Sci. 11 (2018), 1268-1293.


(with R. Wagner and R. Ramlau) Simulation results for a finite element-based cumulative reconstructor, J. Astron. Telesc. Instrum. Syst. 3 (2017), 049001 (7pp).


A new gradient method for ill-posed problems, Numer. Funct. Anal. Optim. 39 (2018), 737-762.


A note on optimal rates for Lavrentiev regularization with adjoint source conditions, ETNA 45 (2016), 420-423.


On Nesterov acceleration for Landweber iteration of linear ill-posed problems, J. Inv. Ill-Posed Problems 25 (2017), 381-390.


(with R. Ramlau) A singular value type decomposition for the atmospheric tomography operator, SIAM J. Appl. Math. 77 (2017), 838-853.


(with S. Hubmer, R. Ramlau, and H. U. Voss), On the parameter estimation problem of magnetic resonance advection imaging, Inverse Problems and Imaging 12 (2018), 205-227.


Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales, J. Inv. Ill-Posed Problems 24 (2016), 393-406.


(with R. Ramlau) On convergence rates for quasi-solutions of ill-posed problems, ETNA 41 (2014), 81-92.


On the smoothness of solutions of a special Neumann problem on nonsmooth domains, Journal of Pure and Applied Mathematics: Advances and Applications 11 (2014), 111-135.


A new cumulative wavefront reconstructor for the Shack-Hartmann sensor, J. Inv. Ill-Posed Problems 21 (2013), 451-476.


On the Shack-Hartmann based wavefront reconstruction: stability and convergence rates of finite-dimensional approximations, J. Inv. Ill-Posed Problems 20 (2012), 591-614.


On the ill-posedness and convergence of the Shack-Hartmann based wavefront reconstruction, J. Inv. Ill-Posed Problems 18 (2010), 551-576.


(with S. Kindermann and R. Ramlau) A singular value decomposition for the Shack-Hartmann based wavefront reconstruction, J. Comput. Appl. Math. 236 (2012), 2186-2199.


(with M. Zhariy, M. Rosensteiner, and R. Ramlau), Cumulative wavefront reconstructor for the Shack-Hartmann sensor, Inverse Problems and Imaging 5 (2011), 893-913.


(with T. Hein, B. Hofmann, S. Kindermann, and U. Tautenhahn) Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces, Appl. Anal. 89 (2010), 1729-1743.


Modified Tikhonov regularization for nonlinear ill-posed problems in Banach spaces, J. Integral Equations Appl. 22 (2010), 341-351.


On enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces, Inverse Problems 25 (2009), 065009 (10pp).


On the convergence of a new heuristic parameter selection criterion for general regularization methods, Inverse Problems 24 (2008), 055005 (10pp).


(with S. Kindermann), On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization, Inverse Problems and Imaging 2 (2008), 291-299.


(with H. K. Pikkarainen), Convergence results for the Bayesian inversion theory, J. Inv. Ill-Posed Problems 16 (2008), 601-613.


(with H. K. Pikkarainen), Convergence rate for the Bayesian inversion theory, PAMM 7 (2007), 1080103-1080104.


Identification of a temperature dependent heat conductivity via adaptive grid regularization, J. Integral Equations Appl. 20 (2008), 229-242.


Solution of ill-posed problems via adaptive grid regularization: convergence analysis, Numer. Funct. Anal. Optim. 28 (2007), 405-423.


Computation of discontinuous solutions of 2D linear ill-posed integral equations via adaptive grid regularization, J. Inv. Ill-Posed Problems 15 (2007), 99-106.


(with B. Kaltenbacher), Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions, Inverse Problems 22 (2006), 1105-1119.


Estimation of discontinuous solutions of ill-posed problems via adaptive grid regularization, J. Inv. Ill-Posed Problems 14 (2006), 705-716.


(with H. Egger), Preconditioning Landweber iteration in Hilbert scales, Numer. Math 101 (2005), 643-662.


(with S. Kindermann), On the estimation of discontinuous solutions of parameter identification problems, in: M. Yamamoto and J. Cheng, eds., 2nd International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches, Journal of Physics, Bristol, 2005, 83-92.


(with S. Kindermann), Parameter identification by regularization for surface representations via the moving grid approach, SIAM J. Control Optim. 42 (2003), 1416-1430.


Estimation of discontinuous solutions of ill-posed problems by regularization for surface representations: numerical realization via moving grids, in: Y.C. Hon, M. Yamamoto, J. Cheng, and J.Y. Lee, eds., Recent Development in Theories and Numerics, International Conference on Inverse Problems, World Scientific Publisher, Singapore, 2003, 67-83.


(with M. Burger), Analysis of Tikhonov regularization for function approximation by neural networks, Neural Networks 16 (2003), 79-90.


(with B. Kaltenbacher and A.G. Ramm), Convergence rates of the continuous regularized Gauss-Newton method, J. Inv. Ill-Posed Problems 10 (2002), 261-280.


(with S. Kindermann), Estimation of discontinuous parameters of elliptic partial differential equations by regularization for surface representations, Inverse Problems 17 (2001), 789-803.


(with M. Burger), Error bounds for approximation with neural networks, J. Approx. Theory 112 (2001), 235-250.


(with S. Kindermann), Regularization for surface representations of discontinuous solutions of linear ill-posed problems, Numer. Funct. Anal. Optim. 22 (2001), 79-105.


On Landweber iteration for nonlinear ill-posed problems in Hilbert scales, Numer. Math. 85 (2000), 309-328.


(with S. Kindermann), Identification of discontinuous parameters by regularization for curve representations, Inverse Problems 15 (1999), 1559-1572.


(with S. Kindermann), Each BV-function is representable by an H1-curve, Technical Report 1/1999, Industrial Mathematics Institute, University of Linz, 1999.


(with O. Scherzer), Regularization for curve representations: uniform convergence for discontinuous solutions of ill-posed problems, SIAM J. Appl. Math. 58 (1998), 1891-1900.


(with O. Scherzer), Reconstruction of discontinuous solutions from blurred data, in: R.L. Barbour, M.J. Carvlin, and M.A. Fiddy , eds., Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, Vol. 3171 of Proceedings of SPIE, SPIE, Washington, 1997, 34-41.


Design of 3d-reflectors for near field and far field problems, in: L.T. Biegler, T.F. Coleman, A.R. Conn, and F.N. Santosa, eds., Large Scale Optimization with Applications, Part I: Optimization in Inverse Problems and Design, Vol. 92 of IMA Volumes in Mathematics and its Applications, Springer, New York, 1997, 101-118.


(with B. Blaschke and O. Scherzer), On convergence rates for the iteratively regularized Gauss-Newton method, IMA Journal of Numer. Anal. 17 (1997), 421-436.


On converse and saturation results for Tikhonov regularization of linear ill-posed problems, SIAM J. Numer. Anal. 34 (1997), 517-527.


(with C. König), Design of a 3d-reflector for the near field problem: a nonlinear inverse problem, Math. Engng. Ind. 5 (1996), 269-279.


(with O. Scherzer), A convergent rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems, ZAA 14 (1995), 369-377.


(with M. Hanke and O. Scherzer), A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995), 21-37.


On converse and saturation results for regularization methods, in: E. Schock , ed., Beiträge zur Angewandten Analysis und Informatik, Helmut Brakhage zu Ehren, Shaker, Aachen, 1994, 262-270.


The iterative solution of a nonlinear inverse problem from industry: Design of reflectors, in: P.J. Laurent, A.Le. Méhauté, and L.L. Schumaker, eds., Curves and Surfaces in Geometric Design, AKPeters, Boston, 1994, 335-342.


(with A. Binder, H.W. Engl, C.W. Groetsch, and O. Scherzer), Weakly closed nonlinear operators and parameter identification in parabolic equations by Tikhonov regularization, Appl. Anal. 55 (1994), 215-234.


(with H. W. Engl), Convergence rates for Tikhonov regularization of implicitly defined nonlinear inverse problems with an application to inverse scattering, in: S. Kubo, ed., Inverse Problems, Techn. Publ., Atlanta, 1993, 90-98.


Modified Tikhonov regularization for nonlinear ill-posed problems leading to optimal convergence rates, in: A.N. Tikhonov, ed., Ill-Posed Problems in Natural Sciences, TVP Sci. Publ., 1992, 104-107.


Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales, Appl. Anal. 46 (1992), 59-72.


(with H. W. Engl), Reflector design as an inverse problem, in: Heiliö, ed., Proc. of the Fifth European Conference for Mathematics in Industry, Teubner, Stuttgart, 1991, 13-24.


(with O. Scherzer), Finite-dimensional approximation of Tikhonov regularized solutions of nonlinear ill-posed problems, Numer. Funct. Anal. Optim. 11 (1990), 85-99.


On the numerical solution of a 3-D magnetostatic scattering problem by boundary integral methods, COMPEL 9 (1990), 147-150, Suppl. A.


(with H. W. Engl), On an inverse problem from magnetostatics, in: W.L. Hogarth and B.J. Noye, eds., Computational Techniques and Applications: CTAC-89, Hemisphere Publ.Comp., Washington, D.C., 1990, 3-15.


(with H. W. Engl and M. Hanke), Tikhonov regularization of nonlinear differential-algebraic equations, in: P.C. Sabatier, ed., Inverse Methods in Action, Springer, Wien, 1990, 92-105.


Tikhonov regularization for nonlinear ill-posed problems: optimal convergence and finite-dimensional approximation, Inverse Problems 5 (1989), 541-557.


(with H.W. Engl and K. Kunisch), Convergence rates for Tikhonov regularization of nonlinear ill-posed problems, Inverse Problems 5 (1989), 523-540.


(with C.W. Groetsch), Regularization of ill-posed problems: optimal parameter choice in finite dimensions, J. Approx. Theory 58 (1989), 184-200.


(with C.W. Groetsch), Convergence of a general projection method for an operator equation of the first kind, Houston J. Math. 14 (1988), 201-208.


An a-posteriori parameter choice for Tikhonov regularization in the presence of modelling error, Appl. Numer. Math. 4 (1988), 507-519.


When do Sobolev spaces form a Hilbert scale?, Proc. Amer. Math. Soc. 103 (1988), 557-562.


(with H.W. Engl), A parameter choice strategy for (iterated) Tikhonov regularization of ill-posed problems leading to superconvergence with optimal rates, Appl. Anal. 27 (1988), 5-18.


(with J.T. King), A variant of finite-dimensional Tikhonov regularization with a-posteriori parameter choice, Computing 40 (1988), 91-109.


(with H.W. Engl), Convergence rates for Tikhonov regularization in finite-dimensional subspaces of Hilbert scales, Proc. Amer. Math. Soc. 102 (1988), 587-592.


An a-posteriori parameter choice for Tikhonov-regularization in Hilbert scales leading to optimal convergence rates, SIAM J. Numer. Anal. 25 (1988), 1313-1326.


(with M. Hanke and R. März), On the regularization of a class of nontransferable differential-algebraic equations, J. Diff. Equations 73 (1988), 119-132.


Tikhonov regularization of ill-posed linear operator equations on closed convex sets, J. Approx. Theory 53 (1988), 304-320.


Numerical realization of an optimal discrepancy principle for Tikhonov regularization in Hilbert scales, Computing 39 (1987), 43-55.


(with M. Hanke and R. März), On the regularization of linear differential-algebraic equations, in: H.W. Engl and C.W. Groetsch, eds., Inverse and Ill-Posed Problems, Academic Press, New York, 1987, 523-540.


(with H.W. Engl), On projection methods for solving linear ill-posed problems, in: A. Vogel, ed., Model Optimization in Exploration Geophysics, Vieweg, Braunschweig, 1987, 73-92.


(with H.W. Engl), Optimal parameter choice for ordinary and iterated Tikhonov regularization, in: H.W. Engl and C.W. Groetsch, eds., Inverse and Ill-Posed Problems, Academic Press, New York, 1987, 97-125.


Finite-dimensional approximation of constrained Tikhonov-regularized solutions of ill-posed linear operator equations, Math. Comp. 48 (1987), 565-583.


(with H.W. Engl), Eine Variante der Marti-Methode zur Lösung inkorrekt gestellter linearer Integralgleichungen, die optimale Konvergenzraten liefert, ZAMM 66 (1986), 406-408.


(with H.W. Engl), An improved version of Marti's method for solving ill-posed linear integral equations, Math. Comp. 45 (1985), 405-416.


(with H.W. Engl), Optimal discrepancy principles for the Tikhonov regularization of integral equations of the first kind, in: G. Hämmerlin and K.H. Hoffmann, eds., Constructive Methods for the Practical Treatment of Integral Equations, Birkhäuser, Basel, 1985, 120-141.



Theses


Konvergenzraten und optimale Parameterwahl bei der Tikhonov Regularisierung linearer und nichtlinearer inkorrekt gestellter Probleme, Habilitationsschrift, University of Linz, 1988.


Tikhonov-Regularization of Ill-Posed Linear Operator Equations on Closed Convex Sets, PhD thesis, University of Linz, November 1985, appeared in Verlag der Wissenschaftlichen Gesellschaften Österreichs, Wien, 1986.


Zur Tikhonov-Regularisierung von linearen Operatorgleichungen, Master's thesis, University of Linz, July 1984.