My Math Forum check if set of nonlinear equ. has only the trivial solution

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 November 19th, 2008, 04:28 PM #1 Newbie   Joined: Nov 2008 Posts: 1 Thanks: 0 check if set of nonlinear equ. has only the trivial solution Hi guys, When I solve equations 3,4,5,6 I'm getting small values for x(1),x(2),x(3),x(4). Using fsolve in matlab I tried different starting values x0, and solutions are in the order of 1e-3 and depend on the starting value. How can I tell if the small values are approximating the trivial solution (because of limited accuracy during the calculation), or if there are several solutions close to the trivial solution? Since I know that there is only the trivial solution when using equation 1,2,3,4,5,6 I calculated x solving all equations and found x in the order of 1e-9. In summary, I want to find out if there is only the trivial solution when solving equations 3,4,5,6. c2=-0.27215029; c3=0.09718148; c5=2.62373636; c6=0.80306059; a1 = -0.2525 a2 = 0.0543 a3 = -0.0264 (1) c2*x(1)+c3*x(3)=0 (2) c2*x(2)+c3*x(4)=0 (3) c5*x(1)+c6*x(3)=0 (4) c5*x(2)+c6*x(4)=0 (5) a1*x(1)*x(2)+a2*x(3)*x(4)-a3*(x(1)*x(4)+x(2)*x(3))=0 (6) a1*(x(2)^2-x(1)^2)+a2*(x(4)^2-x(3)^2)-2*a3*(x(2)*x(4)-x(1)*x(3))=0 Best Regards, Peter matlab code: x0 = [rand(1);rand(1);rand(1);rand(1)]; options=optimset('Display','iter','TolFun',1e-20 ); % Option to display output [x,fval] = fsolve(@my_fun,x0,options); function F=my_fun(x) c2=-0.27215029; c3=0.09718148; c5=2.62373636; c6=0.80306059; a1 = -0.2525 a2 = 0.0543 a3 = -0.0264 F=[ c2*x(1)+c3*x(3); c2*x(2)+c3*x(4); c5*x(1)+c6*x(3); c5*x(2)+c6*x(4); a1*x(1)*x(2)+a2*x(3)*x(4)-a3*(x(1)*x(4)+x(2)*x(3)); a1*(x(2)^2-x(1)^2)+a2*(x(4)^2-x(3)^2)-2*a3*(x(2)*x(4)-x(1)*x(3))];

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