[SciPy-dev] Asking about aplication GA's on root finding
Pearu Peterson
pearu at cens.ioc.ee
Tue Mar 4 01:59:52 CST 2003
On Tue, 4 Mar 2003, Huang Wen Long wrote:
> Now I am taking a subject called Mathematical Modelling which the students
> devided into groups and each group handle one project. While doing our
> project, we are facing a problem to solve system of non-linear equations
> such as : - F1(x,y,z) = z*exp(2*x) + z*y
> - F2(x,y,z) = x^2 +3*x*y^2
> .
> .
> .
It's a bit OT but may be the purpose of this home work is to learn that
one should not blindly reach for numerics to solve problems without doing
analysis first ;)
Assume z!=0 then from F1=0 follows y=-exp(2*x)
Assume x!=0 then from F2=0 follows x=-3*y^2
Now solve the following subproblem
y=-exp(-6*y^2) (*)
numerically using fixed-point method, for example:
y(0)=-0.5 # initial guess
y(n+1)=-exp(-6*y(n)^2)
To see that the above problem has a unique solution, plot the l.h.s and
r.h.s of equation (*). You may also learn from this plot why Newton
type methods will not converge with most initial conditions for y.
Continue with the analysis of F3=0, etc. Also study the cases z==0,
x==0, etc. separately.
HTH,
Pearu
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