--- Исходное сообщение --- От кого: "Yosef Meller" <yosef...@post.tau.ac.il> Кому: scipy-u...@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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