Bisection method code - question.

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Yuval
Yuval 2013-12-26
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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回答（1 个）

Matt J
Matt J 2013-12-26
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
Yuval 2013-12-26
编辑：Yuval 2013-12-26
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
I mean, it keeps giving out h=0.9998, even when I change the while condition to (err > 2.009032E-11), for instance.
Matt J
Matt J 2013-12-26
编辑：Matt J 2013-12-26
What data are you using for V,L,r,h1,h2?

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