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Allianz-Gebäude (05.20)
Zimmer 4C-03

Adresse
Hausadresse:
Zimmer 4C-03
Allianzgebäude am Kronenplatz
Kaiserstr. 89-93
D-76133 Karlsruhe

Postadresse:
Karlsruher Institut für Technologie (KIT)
Fakultät für Mathematik
Institut für Angewandte und Numerische Mathematik
Arbeitsgruppe 3: Wissenschaftliches Rechnen
Kaiserstr. 89-93
D-76133 Karlsruhe

Öffnungszeiten:
Mo-Fr 9-12 Uhr

Tel.: 0721 608 - 42062

Fax.: 0721 608 - 43197

Publikationen von/Publications by Andreas Rieder

Preprints and Work in Progress
  1. Adaptive wavelet collocation method for simulation of time dependent Maxwell's equations, preprint PDF with H. Li, K. Hiremath, and W. Freude
  2. Geometric reconstruction in bioluminescene tomography, preprint PDF, with T. Kreutzmann
  3. The approximate inverse in action IV: semi-discrete equations in a Banach space setting, PDF, Inverse Problems (to appear), with T. Schuster and F. Schöpfer
  4. A Kaczmarz version of the inexact Newton regularization REGINN, work in progress, with A. Leitão
  5. A convergence analysis of the Newton-type regularization CG-REGINN with application to impedance tomography, PDF, IWRMM Preprint 07/01, with A. Lechleiter.

Papers (refereed)
  1. Local inversion of the Sonar transform regularized by the approximate inverse, Inverse Problems 27 (2011) 035006, with Todd Quinto and Thomas Schuster.
  2. Towards a general convergence theory for inexact Newton regularizations, Numer. Math. 114(3), 521-548, 2010, with A. Lechleiter.
  3. Newton regularization for impedance tomography: convergence by local injectivity, Inverse Problems 24 (2008) 065009, with A. Lechleiter.
  4. Shape from specular reflections and optical flow, Int. J. Comput. Vis. 80(2), 226-241, 2008, with J. Lellman, J. Balzer and J. Beyerer.
  5. Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion, Numer. Math. 108(1), 151-175, 2007, with A. Schneck.
  6. Newton regularizations for impedance tomography: a numerical study, Inverse Problems 22(6), 1967-1987, 2006, with A. Lechleiter.
    Chosen by IOPSelect.
  7. Inexact Newton regularization using conjugate gradients as inner iteration, SIAM J. Numer. Anal. 43, 604-622, 2005.
  8. Runge-Kutta integrators yield optimal regularization schemes, Inverse Problems, 21(2), 453-471, 2005.
  9. Approximate inverse in action III: Doppler tomography, Numer. Math. 97, 353-378, 2004, with Th. Schuster.
  10. The semi-discrete filtered backprojection algorithm is optimal for tomographic inversion, SIAM J. Numer. Anal. 41, 869-892, 2003, with A. Faridani.
  11. Approximate inverse in action II: convergence and stability, Math. Comput. 72, 1399-1415, 2003, with Th. Schuster.
  12. Split-step wavelet collocation method for nonlinear optical pulse propagation, IEICE Trans. on Electronics, special issue on "Signals, Systems, and Electronics Technology", E85-C(3), 534-543, 2002, with T. Kremp, A. Killi, and W. Freude.
  13. On filter design principles in 2D computerized tomography, in "Radon Transforms and Tomography", E. T. Quinto et al. (eds.), Contemporary Mathematics 278, AMS Publications, 207-226, 2001.
  14. Classification of endocardial electrograms using adapted wavelet packets and neural networks, Annals of Biomedical Engineering, 2001, with D. Strauß, Y. Manoli, and J. Jung.
  15. On convergence rates of inexact Newton regularizations, Numer. Math. 88(2), 347-365, 2001.
  16. A promising approach to signal dicrimination in electrocardiology: adapted multiresolution signal decompositions, Applied Signal Process. 6(4), 182-193, 1999 (appeared March 2001), with D. Strauß, Th. Sinnwell, Y. Manoli, and J. Jung.
  17. Embedding and a-priori wavelet adaptivity for Dirichlet problems, M^2AN, 34(6), 1189-1202, 2000.
  18. Approximate inverse in action with an application to 2D-computerized tomography, SIAM J. Numer. Anal., 37(6), 1909-1929, 2000, with Th. Schuster.
  19. Approximate inverse meets local tomography, Math. Meth. Appl. Sci., 23, 1373-1387, 2000, with R. Dietz and Th. Schuster.
  20. On the regularization of nonlinear ill-posed problems via inexact Newton iterations, Inverse Problems 15(1), 309-327, 1999.
  21. A painless and direct way from integral to discrete fast wavelet transforms, ZAMM, 8(11), 781-785, 1998.
  22. A domain embedding method for Dirichlet problems in arbitrary space dimension, M^2AN, 32(4), 405-431, 1998.
  23. Wavelet multilevel solvers for linear ill-posed problems stabilized by Tikhonov regularization, in "Multiscale Wavelet Methods for Partial Differential Equations", W. Dahmen, A. Kurdila, and P. Oswald (eds.), Academic Press, San Diego, 1997, 347-380.
  24. On embedding techniques for 2nd-order elliptic problems, in "Computational Science for the 21st Century", M.-O. Bristeau et al. (eds.), Wiley, Chichester, 1997, 179-188.
  25. Wavelet-accelerated Tikhonov-Phillips regularization with applications, in "Inverse Problems in Medical Imaging and Nondestructive Testing", H. W. Engl, A. K. Louis, and W. Rundell (eds.),Springer-Verlag, Wien 1997, 134-159, with P. Maaß.
  26. A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization, Numer. Math. 75(4), 501-522, 1997.
  27. A wavelet multigrid preconditioner for Dirichlet boundary-value problems in general domains, M^2AN, 30(6), 711-729, 1996, with R. Glowinski, R. O. Wells Jr. and X. Zhou.
  28. On the robustness of the damped V-cycle of the wavelet frequency decomposition multigrid method, Computing 53(2), 155-171, 1994, with X. Zhou.
  29. A wavelet approach to robust multilevel solvers for anisotropic elliptic problems, Applied and Computational Harmonic Analysis, 1(4), 355-367, 1994, with R. O. Wells Jr. and X. Zhou.
  30. Multilevel methods based on wavelet decompositions, East-West J. Numer. Math., 2(4), 313-330, 1999.
  31. The high frequency behaviour of continuous wavelet transforms, Applicable Analysis, 52, 125-141, 1994.
  32. The wavelet transform on Sobolev spaces and its approximation properties, Numer. Math. 58, 875-894, 1991.
  33. Incomplete data problems in X-ray computerized tomography, Numer. Math. 56, 371-383, 1989, with A. K. Louis.

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Proceedings
  1. Local SONAR inversion, Oberwolfach Reports 7(2), 1058-1060, 2010, with Todd Quinto and Thomas Schuster.
  2. Tangential cone condition for electrical impedance tomography, Oberwolfach Reports 4(1), 719-721, 2007, with Armin Lechleiter.
  3. Optimality of the fully discrete filtered backprojection algorithm in 2D, Oberwolfach Reports 3(3), 2101-2104, 2006, with Arne Schneck.
  4. Optimal coating of laser mirrors for the generation of ultrashort laser pulses, PAMM Proc. Appl. Math. Mech. 5, 643-644, 2005, with J. Brunk and U. Morgner.
  5. Adaptive multiresolution split-step wavelet collocation method for nonlinear optical pulse propagation, "Proceedings Lasers and Electro-Optics" (CLEO 2002), Long Beach (CA), Session CThO, with T. Kremp, A. Killi, and W. Freude.
  6. Evaluating the reconstruction limits and the effect of modeling errors in noninvasive cardiac source imaging, Biomedizinische Technik, 46(2), 88-90, 2001, with O. Skipa, N. Holtrop, C. D. Werner, F. B. Sachse, O. Dössel.
  7. Das inverse Problem der Elektrokardiographie: Rekonstruktion realistischer Quellverteilungen, Biomedizinischen Technik, 46(1), 508-509, 2001, with N. Holtrop, O. Skipa, C. D. Werner, F. B. Sachse, O. Dössel.
  8. How to scale reconstruction filters in 2D-computerized tomography, ZAMM 81(Supplement 3), S621-S622, 2001.
  9. The recognition of antegrade and retrograde atrial activation patterns using hybrid wavelet-neural network schemes, Proceedings "Computers in Cardiology 2000" Boston, IEEE, with D. Strauß and J. Jung.
  10. A unified convergence theory for the iterative regularization of nonlinear ill-posed problems, ZAMM 80(Supplement 1), S245-S248, 2000.
  11. Additive and multiplicative Schwarz algorithms for linear ill-posed problems, ZAMM 76(Supplement 1), 187-190, 1996.
  12. A preconditioned CG-method for wavelet-Galerkin discretizations of elliptic problems, ZAMM 75, S683 - S684, 1995, with R. Glowinski, R. O. Wells Jr., and X. Zhou.
  13. On the wavelet frequency decomposition method in "Wavelet Applications", Harold H. Szu (ed.), Proc. SPIE 2242, 14-18, 1994,with R. O. Wells Jr. and X. Zhou.
  14. Wavelet analysis of auscultory blood pressure signals, Abstracts of the second European Conference on Engineering and Medicine 1993, Elsevier, 1993, 322-323, with H. Hammer, P. Maaß and J.-U. Meyer.
  15. Approximationseigenschaften der Wavelet-Transformation, ZAMM 70(6), T577-T578, 1999.

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Books and Monographs
  1. Keine Probleme mit Inversen Problemen, Vieweg, 2003.
  2. Wavelets - Theorie und Anwendungen, Teubner, Stuttgart, 2. Auflage, 1998, with A. K. Louis and P. Maaß.
  3. Wavelet-Methoden für schlecht-gestellte und elliptische Probleme, Annales Universitatis Saraviensis, Series Mathematicae 7(4), 75-194, 1997.
  4. Wavelets - Theory and Applications, Wiley, 1997, with A. K. Louis and P. Maaß.

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