×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

NonLinear System of Equations Problem

NonLinear System of Equations Problem

NonLinear System of Equations Problem

(OP)
Hi guys,
I have a problem with a nonlinear system equations solve.
I'm not able to find a good solution to my system, and I don't realize if the algorithms used are good for the system.
I wrote the system of equation in a Matlab file, and sure I used the fsolve command. Below is the Mfile (nonlinear system):

function F = myfun (x)
F=[(2e-2)-0-(3.5e-3)*((((x(2)/345)*sin(x(1)))/sqrt(1-(x(2)/345)^2*(sin(x(1)))^2))+(((x(3)/345)*sin(x(1)))/sqrt(1-(x(3)/345)^2*(sin(x(1)))^2)));
(1e-2)-0-(3.5e-3)*((((x(2)/345)*sin(x(4)))/sqrt(1-(x(2)/345)^2*(sin(x(4)))^2))+(((x(3)/345)*sin(x(4)))/sqrt(1-(x(3)/345)^2*(sin(x(4)))^2)));
(sqrt(1+((x(2)/345)^2*(sin(x(1)))^2)/(1+(x(2)/345)^2*(sin(x(1)))^2))/x(2)+sqrt(1+((x(3)/345)^2*(sin(x(1)))^2/(1+(x(3)/345)^2*(sin(x(1)))^2)))/x(3))*(3.5e-3)-(42.68e-6);
(sqrt(1+((x(2)/345)^2*(sin(x(4)))^2)/(1+(x(2)/345)^2*(sin(x(4)))^2))/x(2)+sqrt(1+((x(3)/345)^2*(sin(x(4)))^2/(1+(x(3)/345)^2*(sin(x(4)))^2)))/x(3))*(3.5e-3)-(28.58e-6)];

 
I chose a start point x0=[0.1;50;50;0.1]; and I launched the fsolve command: x=fsolve(@myfun,x0,option)
where in option is definite the algorithm choose for the solution.

Using the Gauss-Newton algorithm the exit message and the solution was:
Conditioning of Gradient Poor - Switching To LM method
Warning: Matrix is singular to working precision.
> In optim\private\nlsq at 269
  In fsolve at 300
     2         402             NaN       1e-008             NaN              0
Maximum number of function evaluations exceeded. Increase OPTIONS.MaxFunEvals.

x =13.6589;50.0206;50.0206;6.8449



Using the Levenberg-Marquardt algorithm the exit message and the solution was:
Optimizer appears to be converging to a minimum that is not a root:
Sum of squares of the function values is > sqrt(options.TolFun).
Try again with a new starting point.

x =1.4522;50.0234;50.0234;1.3728

Besides in all trials I made changing the start point, the result is always very close to that x0 chose (I think it is not so good).
Now I need of a tip to understand which is the right algorithm solver to use for my problem, and how to choose a good start point.
How can I find the right solution to my nonlinear system?

Thanks in advance.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources