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September 27, 2008

Bibliography

1
J. Baumeister and A. Leitao.
Iterative methods for ill-posed problems modeled by PDE's.
Journal of Inverse and Ill-Posed Problems, 9(1):1-17, 2001.
2
H. Benameur, M. Burger, and B. Hackl.
Level set methods for geometric inverse problems in linear elasticity.
Inverse Problems, 20(3):673-696, 2004.
3
H. Benameur, M. Burger, and B. Hackl.
Cavity identification in linear elasticity and thermoelasticity.
Mathematical Methods in the Applied Sciences, 30(6):625-647, 2007.
4
H. Benameur and B. Kaltenbacher.
Regularization of parameter estimation by adaptive discretization using refinement and coarsening indicators.
Journal of Inverse and Ill-Posed Problems, 10(6):561-583, 2002.
5
N. Bila.
Application of symmetry analysis to a pde arising in the car windshield design.
SIAM Journal on Applied Mathematics, 65:113-130, 2004.
6
N. Bila and J. Niesen.
On a new procedure for finding nonclassical symmetries.
Journal of Symbolic Computation, 38:1523-1533, 2004.
7
M. Burger.
Iterative regularization of a parameter identification problem occurring in polymer crystallization.
SIAM J. Numer. Anal., 39(3):1029-1055, 2001.
8
M. Burger.
A level set method for inverse problems.
Inverse Problems, 17:1327-1356, 2001.
9
M. Burger.
A framework for the construction of level set methods for shape optimization and reconstruction.
Interfaces and Free Boundaries, 5:301-329, 2003.
10
M. Burger.
Growth of multiple crystals in polymer melts.
European J. Appl. Math., 15:347-363, 2004.
11
M. Burger.
Levenberg-Marquardt level set methods for inverse obstacle problems.
Inverse Problems, 20:259-282, 2004.
12
M. Burger.
Surface diffusion including free adatoms.
Comm. Math. Sci., 4:1-51, 2006.
13
M. Burger and V. Capasso.
Mathematical modelling and simulation of non-isothermal crystallization of polymers.
Mathematical Models and Methods in Applied Sciences, 11:1029-1054, 2001.
14
M. Burger, V. Capasso, and G. Eder.
Modelling crystallization of polymers in temperature fields.
Z. Angew. Math. Mech., 82:51-63, 2002.
15
M. Burger, V. Capasso, and H. W. Engl.
Inverse problems related to crystallization of polymers.
Inverse Problems, 15:155-173, 1999.
16
M. Burger, V. Capasso, and A. Micheletti.
Optimal control of polymer morphologies.
J. Eng. Math., 49:339-358, 2004.
17
M. Burger, V. Capasso, and L. Pizzocchero.
Mesoscale averaging of nucleation and growth models.
Multiscale Model. Simul., 5(2):564-592, 2006.
18
M. Burger, V. Capasso, and S. Salani.
Modelling multi-dimensional crystallization of polymers in interaction with heat transfer.
Nonlinear Analysis, Series B, Real World Applications, 3:139-160, 2002.
19
M. Burger and H. W. Engl.
Training neural networks with noisy data as an ill-posed problem.
Advances in Computational Mathematics, 13:335-354, 2000.
20
M. Burger, H. W. Engl, J. Haslinger, and U. Bodenhofer.
Regularized data-driven construction of fuzzy controllers.
J. Inverse and Ill-posed Problems, 10:319-344, 2002.
21
M. Burger, H. W. Engl, A. Leitao, and P. Markowich.
On inverse problems for semiconductor equations.
Milan J. Math., 72:273-314, 2004.
22
M. Burger, H. W. Engl, P. A. Markowich, and P. Pietra.
Identification of doping profiles in semiconductor devices.
Inverse Problems, 17:1765-1795, 2001.
23
M. Burger, K. Frick, S. Osher, and O. Scherzer.
Inverse total variation flow.
Multiscale Model. Simul., 6(2):366-395, 2007.
24
M. Burger, G. Gilboa, S. Osher, and J. Xu.
Nonlinear inverse scale space methods.
Commun. Math. Sci, 4(1):179-212, 2006.
25
M. Burger, B. Hackl, and W. Ring.
Incorporating topological derivatives into level set methods.
J. Comp. Phys., 194(1):344-362, 2004.
26
M. Burger, F. Hausser, C. Stöcker, and A. Voigt.
A level set approach to anisotropic flows with curvature regularization.
J. Comp. Phys, 2007.
to appear.
27
M. Burger and M. Hintermueller.
Projected gradient flows for bv / level set relaxation.
PAMM, 5:11-14, 2005.
28
M. Burger and A. Hofinger.
Regularized greedy algorithms for network training with data noise.
Computing, 74(1):1-22, 2005.
29
M. Burger and B. Kaltenbacher.
Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems.
SIAM J. Numer. Anal., 44:153-182., 2006.
30
M. Burger and W. Mühlhuber.
Iterative regularization of parameter identification problems by SQP-methods.
Inverse Problems, 18:943-970, 2002.
31
M. Burger and W. Mühlhuber.
Numerical approximation of an SQP-type method for parameter identification.
SIAM J. Numer. Anal., 40(5):1775-1797, 2002.
32
M. Burger and A. Neubauer.
Error bounds for approximation with neural networks.
Journal of Approximation Theory, 112:235-250, 2001.
33
M. Burger and A. Neubauer.
Analysis of Tikhonov regularization for function approximation by neural networks.
Neural Networks, 16:79-90, 2003.
34
M. Burger and S. Osher.
Convergence rates of convex variational regularization.
Inverse problems, 20:1411-1421, 2004.
35
M. Burger and S. Osher.
A survey on level set methods for inverse problems and optimal design.
European J. Appl. Math., 16(2):263-301, 2005.
36
M. Burger, S. Osher, and E. Yablonovitch.
Inverse problem techniques for the design of photonic crystals.
IEICE Transactions E, 87, 2004.
37
M. Burger and R. Pinnau.
Fast optimal design of semiconductor devices.
SIAM J. Appl. Math., 64:108-126, 2004.
38
M. Burger and O. Scherzer.
Regularization methods for blind deconvolution and blind source separation problems.
Mathematics of Control, Signals and Systems, 14:358-383, 2001.
39
R. Chapko and P. Kügler.
A comparison of the Landweber method and the Gauss-Newton method for an inverse parabolic boundary value problem.
J. Comput. Appl. Math., 169:183-196, 2004.
40
P. Deuflhard, H. W. Engl, and O. Scherzer.
A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions.
Inverse Problems, 14(5):1081-1106, 1998.
41
H. Egger.
Semiiterative regularization in Hilbert scales.
SIAM J. Numer. Anal., 44:66-81, 2006.
42
H. Egger.
Fast fully iterative Newton-type methods for inverse problems.
J. Inv. Ill-posed Probl., 15:257-275, 2007.
43
H. Egger.
Preconditioning CGNE iteration for inverse problems.
Num. Lin. Alg. Appl., 14(3):183-196, 2007.
44
H. Egger.
Y-scale regularization.
SINUM, 2007.
accepted.
45
H. Egger and H. W. Engl.
Tikhonov regularization applied to the inverse problem of option pricing: Convergence analysis and rates.
Inverse Problems, 21:1027-1045, 2005.
46
H. Egger, H. W. Engl, and M. V. Klibanov.
Global uniqueness and Hölder stability for recovering a nonlinear source term in a parabolic equation.
Inverse Problems, 21:271-290, 2005.
47
H. Egger, T. Hein, and B. Hofmann.
On decoupling of volatility smile and term structure in inverse option pricing.
Inverse Problems, 22:1247-1259, 2006.
48
H. Egger and A. Neubauer.
Preconditioning Landweber iteration in Hilbert scales.
Numerische Mathematik, 101:643-662, 2005.
49
H. Engl, P. Fusek, and S. Pereverzev.
Natural linearization for the identification of nonlinear heat transfer laws.
Journal of Inv. and Ill-Posed Problems, 13:567-582, 2005.
50
H. Engl and A. Leitao.
A Mann iterative method for elliptic Cauchy problems.
Numer. Funct. Anal. and Optimiz., 22(7-8):861-884, 2001.
51
H. W. Engl.
Calibration problems - an inverse problem view.
Wilmott magazine, pages 16-20, 2007.
52
H. W. Engl, M. Burger, and R. Eisenberg.
Inverse problems related to ion channel selectivity.
SIAM Journal on Applied Mathematics, 67:960-989, 2007.
53
H. W. Engl and T. Felici.
On shape optimization of optical waveguides using inverse problems techniques.
Inverse Problems, 17:1141-1162, 2001.
54
H. W. Engl, A. Hofinger, and S. Kindermann.
Convergence rates in the Prokhorov metric for assessing uncertainty in ill-posed problems.
Inverse Problems, 21:399-412, 2005.
55
H. W. Engl and P. Kügler.
Identification of a temperature dependent heat conductivity by Tikhonov regularization.
J. of Inverse and Ill-Posed Problems, 10:67-90, 2002.
56
H. W. Engl and P. Kügler.
The influence of the equation type on iterative parameter identification problems which are elliptic or hyperbolic in the parameter.
European Journal on Applied Mathematics, 14:13-38, 2003.
57
H. W. Engl, J. Lu, and P. Schuster.
Inverse bifurcation analysis: application to simple gene systems.
Algorithms for Molecular Biology, 1:11, 2006.
58
H. W. Engl, E. Resmerita, and A. N. Iusem.
The EM algorithm for ill-posed integral equations: a convergence analysis.
Inverse Problems, 23:2575-2588, 2007.
59
H. W. Engl and J. Zou.
A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction.
Inverse Problems, 16(6):1907-1923, 2000.
60
B. Hackl.
Methods for reliable topology changes for perimeter regularized geometric inverse problems.
SIAM J. Num. Anal., 45:2201-2227, 2007.
61
L. He, S. Osher, and M. Burger.
Iterative total variation regularization with non-quadratic fidelity.
J. Math. Imag. Vision, 26:167-184, 2005.
62
A. Hofinger.
Nonlinear function approximation: Computing smooth solutions with an adaptive greedy algorithm.
Journal of Approximation Theory, 43(2):159-175, 2006.
63
A. Hofinger and H. K. Pikkarainen.
Convergence rates for the bayesian approach to linear inverse problems.
Inverse Problems, 23:2469-2484, 2007.
64
A. Hofinger and J. Valdman.
Numerical solution of the two-yield elastoplastic minimization problem.
Computing, 2007.
(accepted).
65
T. Hohage.
Convergence rates of a regularized Newton method in sound-hard inverse scattering.
SIAM J. Numer. Anal., 36:125-142, 1998.
66
T. Hohage.
Regularisation of exponentially ill-posed problems.
Numer. Funct. Anal. Optim., 21:439-464, 2000.
67
T. Hohage.
On the numerical solution of a three-dimensional inverse medium scattering problem.
Inverse Problems, 17(6):1743-1763, 2001.
68
T. Hohage and C. Schormann.
A Newton-type method for a transmission problem in inverse scattering.
Inverse Problems, 14(5):1207-1227, 1998.
69
J. M. J. Huttunen and H. K. Pikkarainen.
Discretization error in dynamical inverse problems: one-dimensional model case.
Journal of Inverse and Ill-posed Problems, 15(4):365-386, 2007.
70
B. Kaltenbacher.
On Broyden's method for nonlinear ill-posed problems.
Numer. Funct. Anal. Opt., 19:807-833, 1998.
71
B. Kaltenbacher.
A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems.
Numer. Math., 79:501-528, 1998.
72
B. Kaltenbacher.
On convergence rates for some iterative regularization methods for an inverse problem for a nonlinear parabolic equation connected with continuous casting of steel.
Journal of Inverse and Ill-Posed Problems, 7:145-164, 1999.
73
B. Kaltenbacher.
A projection-regularized Newton method for nonlinear ill-posed problems with application to parameter identification problems with finite element discretization.
SIAM J. Numer. Anal., 37:1885-1908, 2000.
74
B. Kaltenbacher.
Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems.
Inverse Problems, 16(5):1523-1539, 2000.
75
B. Kaltenbacher.
On the regularizing properties of a full multigrid method for ill-posed problems.
Inverse Problems, 17:767-788, 2001.
76
B. Kaltenbacher.
V-cycle convergence of some multigrid methods for ill-posed problems.
Math. Comput., 72:1711-1730, 2003.
77
B. Kaltenbacher, M. Kaltenbacher, and S. Reitzinger.
Identification of nonlinear B-H curves based on magnetic field computations and multigrid methods for ill-posed problems.
European Journal of Applied Mathematics, 14(1):13-38, 2003.
78
B. Kaltenbacher, A. Neubauer, and A. Ramm.
Convergence rates of the continuous regularized Gauss-Newton method.
J. Inv. Ill-Posed Problems, 10:261-280, 2002.
79
B. Kaltenbacher and J. Schicho.
A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems.
Numerische Mathematik, 93(1):77-107, 2002.
80
B. Kaltenbacher and J. Schöberl.
A saddle point variational formulation for projection-regularized parameter identification.
Numerische Mathematik, 91(4):675-697, 2002.
81
S. Kindermann and A. Leitao.
Regularization by dynamic programing.
J. Inv. Ill-posed Probl., 15:295-310, 2007.
82
S. Kindermann, P. Mayer, H.-J. Albrecher, and H. W. Engl.
Identification of the local speed function in a Levy model for option pricing.
J. Int. Eq. Appl, 2007.
accepted.
83
S. Kindermann and R. Ramlau.
Surrogate functionals and thresholding for inverse interface problems.
J. Inv. Ill-posed Probl., 15:387-402, 2007.
84
P. Kügler.
A derivative-free Landweber iteration for parameter identification in certain elliptic pdes.
Inv. Probl., 19(6):1407-1426, 2003.
85
P. Kügler.
Identification of a temperature dependent heat conductivity from single boundary measurements.
SIAM J. Numer. Anal., 41:1543-1564, 2004.
86
P. Kügler.
A parameter identification problem of mixed type related to the manufacture of car windshields.
SIAM J. Appl. Math., 64:858-877, 2004.
87
P. Kügler.
Convergence rate analysis of a derivative free landweber iteration for parameter identification in certain elliptic pdes.
Numer. Math., 101(1):165-184, 2005.
88
P. Kügler and A. Leitao.
Mean value iterations for nonlinear elliptic Cauchy problems.
Numerische Mathematik, 96:269-293, 2003.
89
A. Leitao.
An iterative method for solving elliptic Cauchy problems.
Numerical Functional Analysis and Optimization, 5-6(21):715-742, 2000.
90
A. Micheletti and M. Burger.
Stochastic and deterministic simulation of nonisothermal crystallization of polymers.
Journal of Mathematical Chemistry, 30:169-193, 2001.
91
S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin.
An iterative regularization method for total variation based image restoration.
Multiscale Modelling and Simulation, 4:460-489, 2005.
92
H. K. Pikkarainen.
State estimation approach to nonstationary inverse problems: discretization error and filtering problem.
Inverse Problems, 22(1):365-379, 2006.
93
T. Seidel and H. W. Engl.
Recovering discrete and continuous parts of the solution of linear ill-posed problems by Tikhonov regularization.
J. of Inverse and Ill-Posed Problems, 7:165-183, 1999.
94
R. Stainko and M. Burger.
Phase-field relaxation of topology optimization with local stress constraints.
SIAM Journal on Control and Optimization, 45(4):1447-1466, 2006.
95
M.-T. Wolfram.
Inverse dopant profiling from transient measurements.
J. Comp. Electr., 2007.
to appear.




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SpezialForschungsBereich SFB F013 | Special Research Program of the FWF - Austrian Science Fund