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

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 November 19th, 2008, 05:28 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))]; Tags check, equ, nonlinear, set, solution, trivial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jones123 Algebra 11 June 21st, 2016 02:22 AM nitin7785 Differential Equations 0 November 7th, 2013 01:22 AM rayman Real Analysis 0 February 18th, 2013 04:41 AM Bucephalus Linear Algebra 10 January 28th, 2012 10:08 PM jones123 Calculus 2 December 31st, 1969 04:00 PM

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