[Numpy-discussion] [SciPy-User] [ANN] Guaranteed solution of nonlinear equation(s)

[Dmitrey]

   --- Исходное сообщение ---
   От кого: "Yosef Meller" <yosefmel at post.tau.ac.il>
   Кому: scipy-user at scipy.org
   Дата: 25 мая 2011, 08:54:16
   Тема: Re: [SciPy-User] [ANN] Guaranteed solution of nonlinear
   equation(s)



     On ??? ????? 24 ??? 2011 13:22:47 Dmitrey wrote:
     >  Hi all,
     >    I have made my free solver interalg (     http://openopt.org/interalg     ) be
     >    capable of solving nonlinear equations and systems of them. Unlike
     >    scipy optimize fsolve it doesn't matter which functions are involved -
     >    convex, nonconvex, multiextremum etc. Even some discontinuous funcs
     >    can be handled. If no solution exists, interalg determines it rather
     >    quickly.
     > 
     >    For more info see      http://forum.openopt.org/viewtopic.php?id=423     
     Interesting. Is there any description of the actual algorithm? I tried looking 
     for it in the link and the openopt site, but couldn't find it.
   

   Algorithm belongs to family of interval methods. Those ones, along
   with Lipschitz methods, are capable of doing the task (searching
   extremum with guaranteed precision), but require extremely much
   computational time and memory, thus are very rarely used. Some ideas
   created and programmed by me increased speed in many orders (see that
   benchmark vs Direct, intsolver and commercial BARON), memory
   consumption also isn't very huge.
   As for solving equations system, currently |f1| + |f2| + |f3| + ... +
   |f_k| is minimized (| . | means abs( . )). I know better way of
   handling nonlinear systems by interalg, but it would take much time to
   write those enhancements (maybe some weeks or even more), my current
   work doesn't allow me to spend so much time for interalg and other
   openopt items development.
   Regards, D.
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