Why is this break not executing for the summation of pi

Question

Alec Bischoff 2020-9-4

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/588829-why-is-this-break-not-executing-for-the-summation-of-pi

关闭： MATLAB Answer Bot 2021-8-20

pie = 0;
for k = 0:100
    eqn = sqrt(12)*((-3)^(-k)/((2*k)+1));
    PrevSum = pie;
    pie = pie + eqn;
    if PrevSum ~= 0 & (PrevSum/pie) < (10^(-8))
        k
        return
    end
end
pie
PrevSum/pie
>>
pie =
   3.141592653589794
ans =
     1

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Alec Bischoff 2020-9-4

PrevSum/pie should eventually get below 10^-8, but my code doesn't seem to.

请先登录，再回答此问题。

Answer 1

Stephan 2020-9-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/588829-why-is-this-break-not-executing-for-the-summation-of-pi#answer_489622

在 MATLAB Online 中打开

You never reach the value of your ratio of PrevSum/pie. I inserted 2 lines, the first saves the ratio in every single run of your loop, the second plots the ratio over the variable k. This helps you to understand whats going wrong. You will have to think about another criteria to stop the loop, when the maximum deviation is reached:

pie = 0;
for k = 0:100
    eqn = sqrt(12)*((-3)^(-k)/((2*k)+1));
    PrevSum = pie;
    pie = pie + eqn;
    error_rate(k+1) = PrevSum/pie;
    if PrevSum ~= 0 && (PrevSum/pie) < (10^(-8))
        k
        return
    end
end
pie
PrevSum/pie
plot(0:100,error_rate)

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

Answer 2

Alan Stevens 2020-9-4

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/588829-why-is-this-break-not-executing-for-the-summation-of-pi#answer_489628

在 MATLAB Online 中打开

PrevSum/pie should tend to 1. abs(PrevSum - pie) should get smaller than 10^-8.

Try

pie = 0;
k = 0;
err = 1;
while err>10^-9
    PrevSum = pie;
    eqn = sqrt(12)*((-3)^(-k)/((2*k)+1));
    pie = PrevSum + eqn;
    err =abs(PrevSum/pie - 1); 
    k = k+1;
end
format long
pie
PrevSum/pie
abs(PrevSum - pie)