Bisection method code - question.

Question

Yuval 2013-12-26

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编辑： Matt J 2013-12-26

Hi, I wrote the following function for solving V=L[arccos(h/r)r^2 - h(r^2-h^2)^0.5] using the bisection method. However, as I execute the program it gets stuck, yet I cannot figure out why. I'd appreciate any comments.

function h = volume(V,L,r,h1,h2)
h=(h1+h2)/2;
err=abs(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2)));
while (err > 0.01)
    if (V-L*(acosd(h1/r)*r^2-h1*sqrt(r^2-h1^2))*(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2))) < 0)
        h2=h;
    else
        h1=h;
    end
    h=(h1+h2)/2;
    err=abs(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2)));
end

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Answer 1

Matt J 2013-12-26

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I think you're just missing some parentheses in

 if (V-L*(acosd(h1/r)*r^2-h1*sqrt(r^2-h1^2))*(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2))) < 0)

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Yuval 2013-12-26

编辑：Yuval 2013-12-26

在 MATLAB Online 中打开

Okay, now the following code doesn't get stuck but the answer seems to be inaccurate. Any idea why?

function h = volume(V,L,r,h1,h2)
h=(h1+h2)/2;
err=abs(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2)));
while (err > 0.01)
    if ((V-L*(acosd(h1/r)*r^2-h1*sqrt(r^2-h1^2)))*(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2))) < 0)
        h2=h;
    else
        h1=h;
    end
    h=(h1+h2)/2;
    err=abs(V-L*(acosd(h/r)*r^2-h*sqrt(r^2-h^2)));
end