W dniu 2012-09-15 04:51, Robert Dodier pisze:
> Adam Majewski<adammaj1<at> o2.pl> writes:
>
>> Curve3b:GiveListAngle(3,1,center3[2],50)
>> "mnewton: the process doesn't converge or it converges too slowly."
>
> Well, trace(mnewton) shows that it processes several problems
> successfully but then it fails on this one:
>
> mnewton ([z^4+2*c*z^2-z+c^2+c, 4*z^3+4*c*z - %i*sin(2.0*%pi) - cos(2.0*%pi)],
> [c, z], [-1, 0]);
> => mnewton: the process doesn't converge or it converges too slowly.
>
> But I find that if you just change the initial point, it succeeds:
>
> mnewton ([z^4+2*c*z^2-z+c^2+c, 4*z^3+4*c*z - %i*sin(2.0*%pi) - cos(2.0*%pi)],
> [c, z], [0, 1]);
> => [[c = 7.37444285991106E-34*%i+0.25,z = 0.5-6.122503540205582E-17*%i]]
>
> Maybe the solution of the preceding problem is a good starting
> point for the next one? I don't know.
>
> As a separate issue, maybe you want to make the increment of each
> step a rational number instead of float, so that you would get
> sin(2*%pi) and cos(2*%pi) which will simplify. I don't think it
> will make much practical difference.
>
> Hope this helps,
>
> Robert Dodier
Thank you for an answer.
You are right the the problem is related with starting point.
Curves ( list of points) 3a, 3b and 3c are computed from the same system
of equations, only starting point differs.
Curve3a:GiveListAngle(3,1, center3[1], 10)$
Curve3b:GiveListAngle(3,1, center3[2], 50)$
Curve3c:GiveListAngle(3,1, center3[3], 50)$
Curve 3a is computed without problems. Here starting point is floating
point number. In case of other curves starting points are complex
numbers ( see center3) :
center3:[-1.754877666246692760,
-0.12256116687665-0.74486176661974*%i,
-0.12256116687665+0.74486176661974*%i]$
Maybe it is a bug ?
The starting point seems good. It is similar to :
http://facstaff.unca.edu/mcmcclur/papers/CriticalBifurcationPP.pdf
Adam