Using fsolve to solve a system of non-linear equations

Submitted by ritavan on Thu, 03/08/2012 - 20:40

Hi,
I need to solve a system of 8 non-linear equations.
I would like to do that without computing the Jacobian (which is very a large : 8x8 matrix).
I inputted the system of equations successfully in SCILAB but I don't know how to invoke the 'fsolve' function.
http://help.scilab.org/docs/5.3.3/en_US/fsolve.html
Any and all help will be greatly appreciated.
Sincere Thanks.

Here is the code :

deff('[y]=f8(x)',...
['f_1=(1/8)*x(1)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))',...
'f_2=(1/8)(x(1)^2)+(1/7)(x(2)^2)+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/7)*(x(2)*x(4)+x(2)*x(6)+x(2)*x(8)+x(4)*x(6))',...
'f_3=(1/8)*x(1)^2+(1/4)*x(3)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/4)(x(3)*x(4)+x(3)*x(7)+x(3)*x(8)+x(4)*x(7))',...
'f_4=(1/8)*x(1)^2+(1/7)*x(2)^2+(1/4)*x(3)^2+(1/2)*x(4)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/7)*(x(2)*x(4)+x(2)*x(6)+x(2)*x(8)+x(4)*x(6))+(2/4)(x(3)*x(4)+x(3)*x(7)+x(3)*x(8)+x(5)*(7))+x(5)*x(8)',...
'f_5=(1/8)*x(1)^2+(1/4)*x(5)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/4)*(x(5)*x(6)+x(5)*x(7)+x(5)*x(8)+x(6)*x(7))',...
'f_6=(1/8)*x(1)^2+(1/7)*x(2)^2+(1/4)*x(5)^2+(1/2)*x(6)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/7)*(x(2)*x(4)+x(2)*x(6)+x(2)*x(8)+x(4)*x(6))+(2/4)(x(5)*x(6)+x(5)*x(7)+x(5)*x(8)+x(6)*x(7))+(x(6)*x(8))',...
'f_7=(1/8)*x(1)^2+(1/4)*x(3)^2+(1/4)*x(5)^2+(1/2)*x(7)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/4)(x(3)*x(4)+x(3)*x(7)+x(3)*x(8)+x(4)*x(7)+x(5)*x(6)+x(5)*(7)+x(5)*x(8)+x(6)*x(7))+(2/2)*(x(7)*x(8))',...
'f_8=(1/8)*x(1)^2+(1/7)*x(2)^2+(1/4)*x(3)^2+(1/2)*x(4)^2+(1/4)*x(5)^2+(1/2)*x(6)^2+(1/2)*x(7)^2+x(8)^2+(2/8)*(x(1)*x(2)+x(1)*x(3)+x(1)*x(4)+x(1)*x(5)+x(1)*x(6)+x(1)*x(7)+x(1)*x(8)+x(2)*x(3)+x(2)*x(5)+x(2)*x(7)+x(3)*x(5)+x(3)*x(6)+x(4)*x(5))+(2/7)*(x(2)*x(4)+x(2)*x(6)+x(2)*x(8)+x(4)*x(6))+(2/4)(x(3)*x(4)+x(3)*x(7)+x(3)*x(8)+x(4)*x(7)+x(5)*x(6)+x(5)*(7)+x(5)*x(8)+x(6)*x(7))+(2/2)*(x(4)*x(8)+x(6)*x(8)+x(7)*x(8))',...
'y=[f_1;f_2;f_3;f_4;f_5;f_6;f_7;f_8]'])
x0=[0.5;0.5;0.5;0.5;0.5;0.5;0.5;0.5]

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