How to solve singularity problem while using fsolve
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Hi,I am trying to solve for x in a equation using fsolve. Below is the code and equation:
a = 0.1886;
b = 0.6886;
c = 1.1886;
m = 0.31372;
x0 = 0.1;
F = @(x)[(((x-a)/(x-c))^(m))+((x-a)/(x-b))];
options = optimset('Display','iter','MaxFunEvals',1e20,'TolFun',2e-50,'TolX',2e-50);
[xd, fval, exitflag, output]= fsolve(F, x0, options)
However, I am getting 'No solution found' with a message: fsolve stopped because the problem appears to be locally singular. I have tried changing the options parameters and initial guess still getting same output. Any help is appreciated.
Thanks, KB
采纳的回答
John BG
2016-5-26
Try splitting the fsolve approach with real() and imag() because with real() i get something:
..
F = @(x)[real(((x-a)/(x-c))^(m))+((x-a)/(x-b))];
..
[xd, fval, exitflag, output]= fsolve(F, x0, options)
Norm of First-order Trust-region
Iteration Func-count f(x) step optimality radius
0 2 0.366931 1.77 1
1 4 0.000271336 0.207172 0.0421 1
2 6 2.03148e-07 0.00645204 0.00109 1
3 8 1.38596e-13 0.000186725 8.97e-07 1
4 10 7.81816e-26 1.54486e-07 6.74e-13 1
5 12 3.08149e-33 1.16029e-13 1.34e-16 1
Equation solved, inaccuracy possible.
The vector of function values is near zero, as measured by the selected value
of the function tolerance. However, the last step was ineffective.
<stopping criteria details>
xd =
0.30
fval =
-0.00
exitflag =
3.00
output =
iterations: 5.00
funcCount: 12.00
algorithm: 'trust-region-dogleg'
firstorderopt: 0.00
message: 'Equation solved, inaccuracy possible.…'
repeat for the imag() part.
Or alternatively use abs() and arg()
all together, you should catch at least 2 poles on b and c.
If you find this answer of any help solving your question,
please click on the thumbs-up vote link,
thanks in advance
John
更多回答（1 个）
Walter Roberson
2016-5-26
x = 943/5000
The equation is exactly 0 at that point, which corresponds to x = a . However, there is no zero crossing because it goes imaginary until x = c at which point it slopes down from infinity towards 2 (and so never crosses 0 for greater x either)
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