Numerical methods

  • Peter Schneider
  • Jürgen Ehlers
  • Emilio E. Falco
Part of the Astronomy and Astrophysics Library book series (AAL)


Several times, we have run into problems where analytical methods are no longer sufficient to analyze a GL system. Our “standard” problem is the inversion of the lens equation, i.e., to find all the images x for a given source position y. Only in the simplest cases can this be done analytically; in general, one must find all the roots of a two-dimensional system of equations. This is not trivial, in particular because the number of solutions is not known a priori. There are other problems where numerical analysis must be applied, e.g., if one wants to determine the total magnification for an extended source, as a function of its position. This problem is computationally simpler than the standard problem.


Deflection Angle Surface Brightness Source Position Source Plane Image Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Peter Schneider
    • 1
  • Jürgen Ehlers
    • 2
  • Emilio E. Falco
    • 3
  1. 1.Max-Planck-Institut für AstrophysikGarchingGermany
  2. 2.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutPotsdamGermany
  3. 3.Harvard-Smithsonian Center for AstrophysicsCambridgeUSA

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