Journal of Integral Equations and Applications

An Evolutionary Newton Method for Shape Reconstruction

H. Eckel and R. Potthast

Full-text: Open access

Article information

J. Integral Equations Applications, Volume 19, Number 3 (2007), 261-287.

First available in Project Euclid: 27 September 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Eckel, H.; Potthast, R. An Evolutionary Newton Method for Shape Reconstruction. J. Integral Equations Applications 19 (2007), no. 3, 261--287. doi:10.1216/jiea/1190905487.

Export citation


  • D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, second edition, Appl. Math. Sci. 93, Springer-Verlag, Berlin, 199-8.
  • D. Colton and R. Kress, Integral equation methods in scattering theory, Pure Appl. Math., John Wiley & Sons Inc., New York, 198-3.
  • O. Dorn, E.L. Miller and C.M. Rappaport, A shape reconstruction method for electromagnetic tomography using adjoint fields and level sets, Inverse Prob. 16 (2000), 1119-1156.
  • H.W. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems, Math. Appl. 375, Kluwer Academic Publishers, Dordrecht, 199-6.
  • L.J. Fogel, A.J. Owens and M.J. Walsh, Artificial intelligence through simulated evolution, John Wiley, New York, 196-6.
  • W.D. Hillis, Co-evolving parasites improve simulated evolution as an optimization procedure, Articial Life II, 10 (1991), 313-324.
  • T. Hohage, Convergence rates of a regularized Newton method in sound-hard inverse scattering, SIAM J. Numer. Anal. 36 (1999), 125-142 (electronic).
  • --------, Iterative methods in inverse obstacle scattering: regularization theory of linear and nonlinear exponentially ill�posed problems, PhD thesis, Linz, 1999.
  • J.H. Holland, Adaptation in natural and artificial systems, The University of Michigan Press, Ann Arbor, 197-5.
  • J.R. Koza, Genetic programming: On the programming of computers by means of natural selection, MIT Press, Cambridge, 199-2.
  • H. Pohlheim, Evolutionäre Algorithmen-Verfahren, Operatoren, Hinweise aus der Praxis, Springer, Berlin, 199-9.
  • R. Potthast, A fast new method to solve inverse scattering problems, Inverse Prob. 12 (1996), 731-742.
  • --------, A point source method for inverse acoustic and electromagnetic obstacle scattering problems, IMA J. Appl. Math. 61 (1998), 119-140.
  • --------, On the convergence of a new Newton-type method in inverse scattering, Inverse Prob. 17 (2001), 1419-1434.
  • --------, Point sources and multipoles in inverse scattering theory, Chapman & Hall/CRC Research Notes Math. 427, Chapman & Hall/CRC, Boca Raton, Florida, 200-1.
  • --------, A survey on sampling and probe methods for inverse problems, Inverse Problems, Topical Review, 200-6.
  • I. Rechenberg, Evolutionsstrategie-Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, Frommann-Holzboog, Stuttgart, 197-3.
  • H.-P. Schwefel, Evolutionsstrategie und numerische Optimierung, PhD thesis, Technische Universität Berlin, 197-5.