fsolve yields wrong answer

Question

Pooneh Shah Malekpoor 2021-11-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582624-fsolve-yields-wrong-answer

评论： Pooneh Shah Malekpoor 2021-11-10

Hello

It is an example of many equations in my lengthy code. I want to use fsolve to solve it as it is more efficient; however, it yields wrong answer:

F = @(x)((x-20.6667)^2+57.89);
opts = optimoptions('fsolve', 'Display', 'off');
    x(1) = fsolve(@(x) F(x), 0, opts);

in this case it yields x(1)=20.6667 ; howver, it should not yield any solution in real domain!!!!I want to get real domain roots by fsolve.

What should i do? I dont want to use solve as it results in longer run times.

Bests

Pooneh

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Answer 1

Star Strider 2021-11-9

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https://ww2.mathworks.cn/matlabcentral/answers/1582624-fsolve-yields-wrong-answer#answer_827584

在 MATLAB Online 中打开

Give fsolve a complex initial estimate to get a complex root —

F = @(x)((x-20.6667).^2+57.89);
opts = optimoptions('fsolve', 'Display', 'off');
x0 = 1 + 1i;
x(1) = fsolve(@(x) F(x), x0, opts)
x = 20.6667 + 7.6085i

.

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Walter Roberson 2021-11-10

在 MATLAB Online 中打开

format long g
F = @(x)((x-20.6667).^2+57.89);
opts = optimoptions('fsolve', 'Display', 'off');
[x, fval, errorflag, output] = fsolve(@(x) F(x), 0, opts);
x
x = 
          20.6666998416185
fval
fval = 
                     57.89
errorflag
errorflag = 
    -2
output
output = struct with fields:
       iterations: 29
        funcCount: 48
        algorithm: 'trust-region-dogleg'
    firstorderopt: 1.33568026341535e-06
          message: '↵No solution found.↵↵fsolve stopped because the last step was ineffective. However, the vector of function↵values is not near zero, as measured by the value of the function tolerance. ↵↵<stopping criteria details>↵↵fsolve stopped because the sum of squared function values, r, changed by 8.814899e-15↵relative to its initial value; this is less than max(options.FunctionTolerance^2,eps) = 1.000000e-12.↵However, r = 3.351252e+03, exceeds sqrt(options.FunctionTolerance) = 1.000000e-03.↵↵'

Notice the errorflag is negative, indicating a failure. Notice the output message says that the last steps it tried did not do any good, but the function value was not near 0.

If the question is how to find out whether fsolve() solved the problem, then look at errorflag

If the question is how fsolve() figures out that it is not going to be able to solve the problem, then the answer is approximately that it did numeric gradient estimation to get to a place where it could see that the gradient was 0 but that the function was not 0.

Star Strider 2021-11-10

在 MATLAB Online 中打开

The fsolve function will find a complex root if given a complex initial estimate, or if a purely imaginary root is the only root.

One option to eliminate complex numbers could be to take their absolute values —

x = 20.6667 + 7.6085i;
xa = abs(x)
xa = 22.0228

and the other option of course is just to use the real part.

However changing the code to accommodate complex numbers may be the best option, because it will likely provide the most accurate results.

.

Matt J 2021-11-10

Give fsolve a complex initial estimate to get a complex root —

But note that this will only lead to a proper complex-domain solution under certain conditions:

https://www.mathworks.com/help/optim/ug/complex-numbers-in-optimization-toolbox-solvers.html

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Answer 2

Matt J 2021-11-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582624-fsolve-yields-wrong-answer#answer_828384

I want to use fsolve to solve it as it is more efficient; however, it yields wrong answer:

In your example, the function is a polynomial. Is this always the case for you? If so, it is more efficient to use roots(). Moreover, roots() will find all solutions, both real and complex, whereas fsolve can find only one solution.

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Pooneh Shah Malekpoor 2021-11-10

Thank you so much Matt J! your comment made a huge positive impact on my code and its run time has decreased significantly. This is highly appreciated!

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Answer 3

Matt J 2021-11-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1582624-fsolve-yields-wrong-answer#answer_828364

编辑：Matt J 2021-11-10

在 MATLAB Online 中打开

parts=@(z) [real(z);imag(z)];
complx=@(x) complex(x(1),x(2));
F = @(x)parts((complx(x)-20.6667)^2+57.89);
opts = optimoptions('fsolve', 'Display', 'off');
   
x = complx( fsolve(F, [0,0], opts))
x = 20.6667 + 7.6085i