Hello, The question is : what sort of problem do you want to solve ? with what method ?
Is this a pure Newton-(Raphson) method? A) If yes: 1) If you compute in RDF floats (that is: your machine floating points numbers, aka "double" in C), the best you have to do is to use the scipy implementation, and hope (like always with Newton method) that it will converge. It will also be slow, because the F and DF functions will be coded in pure python (maybe, this will not be a problem if you want to solve small problems). I think there is no need to add a new method for RDF. May be creating an optimized method (using cython ?) could be interesting. See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html for the scipy implementation. 2) If you want to compute in an other set of numbers, there is nothing (as far as I know) in Sage. For example, the Newton method can be implemented un interval arithmetic (RealIntervalField or RealBallField). But implementing something a bit generic is certainly not so easy. B) If no: That is to say you are interested by implementing a generalized Newton, or quasi Newton method, something like that... These methods are very specialized, and I am not sure it will be an useful tool. But I can be wrong. Yours, Thierry. Le 02/05/2020 à 00:28, Daniel Khodabakhsh a écrit : > Sorry forgot to give details on the algorithm I want to add. > > Here's a Wikipedia link o > <https://en.wikipedia.org/wiki/Newton%27s_method#Nonlinear_systems_of_equations>n > the subject. > > To summarise, it's an iterative numerical method, similar > to sage.numerical.optimize.find_root > <http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html#sage.numerical.optimize.find_root> > but > whose usage would be closer to sage.symbolic.relation.solve > <http://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/relation.html#sage.symbolic.relation.solve>. > > Not sure if google groups supports LaTeX but here's a try: > $$x_{n+1} = x_{n} - J_F(x_n)^{-1}F(x_n)$$ > > On Friday, May 1, 2020 at 3:09:34 PM UTC-7, Daniel Khodabakhsh wrote: > > Hello, > > I have a generalised implementation of Newton's method for solving a > nonlinear system of equations that I want to add to Sage. > This would be my first potential contribution so I had a few > questions before I can move forward. > > Questions #1: > The reason I wrote an implementation was because I couldn't find > this algorithm in Sage. Before I proceed, could someone confirm that > this indeed doesn't already exist? > > Questions #2: > If it really isn't part of Sage yet, which module should I add this to? > > Once I get this information I'll work on integrating it into the > recommended module and create a new ticket on https://trac.sagemath.org/ > > If I have the process wrong please let me know! > > -- > You received this message because you are subscribed to the Google > Groups "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send > an email to sage-devel+unsubscr...@googlegroups.com > <mailto:sage-devel+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/cd1aa005-abcb-4fcb-a436-5afaac4739a0%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/cd1aa005-abcb-4fcb-a436-5afaac4739a0%40googlegroups.com?utm_medium=email&utm_source=footer>. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/a58ed617-9694-1c4d-1ea7-02822fc64832%40math.univ-lyon1.fr.
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