Re: [Jprogramming] Multidimensional Root Finding with Newton Solver

There's also this - http://code.jsoftware.com/wiki/Scripts/nlls - an implementation of the Levenberg-Marquardt algo that I cribbed from someone who copied it from APL. On Thu, Aug 10, 2017 at 6:47 PM, Don Kelly wrote: > I also suggest that you look at references to the use of NR

Re: [Jprogramming] Multidimensional Root Finding with Newton Solver

I also suggest that you look at references to the use of NR for power system load flow problems which are non-linear and generally expressed in terms of complex numbers in the polar format. These do converge well. I haven't written one in J but one written in APL has 11 readable lines-most

Re: [Jprogramming] Multidimensional Root Finding with Newton Solver

Solving many algebraic equations in many unknowns can be done by eliminating the unknowns one by one obtaining many algebraic equations in one unknown each, and then solving these equations numerically. Example: Two equations in two unknowns. 0 = (x^2)+(y^2)-16 = (y-2) .  0 = y-2 = y(y-2) =

Re: [Jprogramming] Multidimensional Root Finding with Newton Solver

I find it interesting that N-R works for vectors and complex functions (and mixes of both). Just replace all those scalar functions by their vector equivalents: vn=: 1 : '- n * u %. u D.1' I added a scaling factor; it makes the convergence slower, but it fixes problems due to precision-loss.

Re: [Jprogramming] Multidimensional Root Finding with Newton Solver

> Is it also possible to solve a system of equation like the following one… ? Basically, yes. Because not only can x = (x1,x2) be a vector, but so can y = (y1,y2) in this adaptation of your equations: y1 = a*(1-x1) y2 = b*(x2-x1^2) TABULA is an app (distributed as a JAL "addon") which

[Jprogramming] Multidimensional Root Finding with Newton Solver

Hi there, J looks very interesting. I have no previous experience with array languages and, being curious, started to experiment. Now, I would like to solve a system of non-linear equations. I could only examples solving single equations like this one: N=: 1 : '- u % u d. 1' NB. Adverb