using "solve" for a system of nonlinear equations

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I have a set of 6 nonlinear equations as follows (a1,a2,a3,b1,b2,b3 are unknowns). I know that one of the answers of this system must be as following: a1=3, a2=1, a3=3, b1=0.2, b2=0.3, b3=0.4 (it exactly satisfies my equations). When I use "solve" it gives me 4 different set of answers but surprisingly none of them is the above mentioned answer that I am anticipating. In fact "solve" is neglecting at least one of the answers of this system. How can I adjust or use "solve" to give me that answer?
syms a1 a2 a3 b1 b2 b3
X1=0.16;
X2=0.9466667;
X3=2.97;
Z1=2.97;
Z2=0.9866667;
Z3=0.38;
[a1, a2, a3, b1, b2, b3]=solve(X1==b1-b2*b3/a1,X2==a2-b3^2/a1,X3==a3-b2^2/a1,Z1==a1-b2^2/a3,Z2==a2-b1^2/a3,Z3==b3-b1*b2/a3);
a1=eval(a1)
a2=eval(a2)
a3=eval(a3)
b1=eval(b1)
b2=eval(b2)
b3=eval(b3)
2- Do you know any other command or user defined function to use for solving system of nonlinear equations and gives me all the answers ? (does not require initial guess like fsolve)

回答(1 个)

Matt J
Matt J 2014-9-25
编辑:Matt J 2014-9-25
2- Do you know any other command or user defined function to use for solving system of nonlinear equations and gives me all the answers ? (does not require initial guess like fsolve)
No, that's not possible for general nonlinear equations and numerical solvers. The set of solutions can be infinite for example, as in the system
x-y=0
x^2-y^2=0
When I use "solve" it gives me 4 different set of answers but surprisingly none of them is the above mentioned answer that I am anticipating.
What answers does it give you?
  6 个评论
Sayed
Sayed 2014-9-26
No, I am not sure whether the answers are really infinite or not, but it is something important to know. Is there any way to find that or at least find some other answers (with solve or ...)?
Matt J
Matt J 2014-9-26
If you have the Global Optimization Toolbox, you could try MultiStart
This would involve basically rewriting the objective function as a least squares problem. MultiStart then manages the running of a least squares minimization algorithm from many starting points and can find multiple solutions.

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