fsolve for nonlinear equation
in [Matlab]
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From: endah on 14 Mar 2010 00:20 Dear All, I work with fsolve to solve my nonlinear equation--> x^q1*(rg+p-rg*q2+dg*q2)/q2/(rg+p)/(dg+p)+... x*dg*(1-q2)/p^q1/q2/(dg+p)+rg/p^(1+q1)/(rg+p) with tha default of fsolve. my initial guess is x=1, but the message is try again with a new starting guess. but i can't find another that obtains better result. and when I try another parameter (p,q1,q2,..etc) there are some complex numbers. Would you help me to deal with this fsolve? Kind regards Endah
From: Walter Roberson on 14 Mar 2010 04:38 endah wrote: > Dear All, > > I work with fsolve to solve my nonlinear equation--> > > x^q1*(rg+p-rg*q2+dg*q2)/q2/(rg+p)/(dg+p)+... > x*dg*(1-q2)/p^q1/q2/(dg+p)+rg/p^(1+q1)/(rg+p) > > with tha default of fsolve. my initial guess is x=1, but the message is > try again with a new starting guess. but i can't find another that > obtains better result. and when I try another parameter (p,q1,q2,..etc) > there are some complex numbers. What kind of values can q1 and p have? Your solutions are the solutions to x^q1 * (p^(2*q1+1) * (rg + 1 + q2*(dg-rg))) + x^1 * p^(q1+1) * dg * (rg * (1 - q2*(p+1)) + p) + x^0 * p^q1 * rg * q2 * (dg + p) which can be rewritten as A * x^q1 + B * x + C but your A and B and C *will* contain complex quantities if p < 0 (unless p > -1 and q1 is +infinity). In the general algebraic case, the coefficients could potentially contain complex quantities if p > 0 but q1 is not an integer (depends how you write the fraction...) or if p > 0 but q1 is a multiple of 4 or 1 less than a multiple of 4 (because I^4 = 1). These are "avoidable" complex quantities (that is, you could choose to ignore those complex values... though doing so might result in discarding an optimum solution.) If your A, B, and C are all real-valued, then unless q1 = 0 or 1 you run into the possibility of complex values again -- even a simple quadratic can encounter complex values.
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