Matlab实验1-3

本文总阅读量次

Matlab计算圆周率

欧拉级数

收敛速度较慢
形式较为雅观

Euler.m

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format long;
t = 9e7;
d = 1;

while d >= 1e-10
    if d<=1e-9
        t = t + 100;
    else
        t = t + 100000;
    end
    mypi = sqrt(6 * EulerSum(t))
    d = abs(pi - mypi)
end

t

EulerSum.m

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function y = EulerFunc(n)
    sum = 1;

    for index = 2:n
        sum = sum + 1 / (index^2);
    end

    y = sum;
    return
end

另一种计算方式：

Euler2.m

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format long;
t = 0;
d = 1;
s=0;

while d >= 1e-10
    t = t + 1;
    s=s+1/(t^2);
    mypi = sqrt(6 * s)
    d = abs(pi - mypi);
end

t

拉马努金级数

收敛速度极快
只需计算一两步即可到达1e-8的精度

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format long;
n = 0;
d = 1;
s = 0;
sqrt_int = (2 * sqrt(2)) / 9801;

while d >= 1e-8
    s = s + (factorial(4 * n) * (1103 + 26390 * n)) / ((factorial(n)^4) * ((396)^(4 * n)));
    mypi = (sqrt_int * s)^(- 1)
    d = abs(pi - mypi)
    n = n + 1;
end

n

莱布尼茨公式

π4=1−13+15−17+⋅⋅⋅\frac{\pi}4=1-\frac13+\frac15-\frac17+\cdot\cdot\cdot 
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format long;
d = 1;
t = 0;
s = 0;
mypi = 0;

while d >= 1e-2
    s = s + ((-1)^t*(1/(2*t+1)));
    mypi = 4 * s
    d = abs(pi - mypi);
    t = t + 1;
end

t
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