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Science Forum Index » Nonlinear Science Forum » ANN 2x2: A Robust Software for Nonlinear Systems
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 Posted: Thu May 03, 2007 7:37 am |
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We present a software to invert functions from the plane to the plane:
F(x, y) = (b1, b2), for a generic smooth function F. In principle, all
points in the preimage of (b1, b2) are computed. The numerical
inversion is based on the characterization of the critical set C {(x,y) : det DF(x,y) = 0} and its image, and in appropriate techniques
of numerical continuation in situations of controlled interaction with
C. A graphical user interface allows for the study of local and global
properties of the function, both of geometric and analytic nature. The
program uses a substantial amount of mathematics: some singularity
theory dating back to Whitney in the fifties and some combinatorial
topology from the sixties (the Blank-Troyer theorems), among other
things.
The program 2x2 is highly portable: it runs under several platforms,
including Microsoft Windows© and Linux. The numerical routines of 2x2
may be used by third party programs through function calls, without
the graphical user interface.
The program is available at http://www.mat.puc-rio.br/~hjbortol/2x2/
Comments are welcome: Carlos Tomei (tomei@mat.puc-rio.br).
Carlos Tomei -- Nicolau Saldanha -- Humberto José Bortolossi --
Eduardo Teles da Silva. |
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