myborwein.m

algotithm to calculate pi

function f=myborwein(n)
a(1)=6-4*sqrt(2);
y(1)=sqrt(2)-1;
for k=1:n
    y(k+1)=(1-(1-y(k)^4)^(0.25))/(1+(1-y(k)^4)^(0.25));
    a(k+1)=a(k).*((1+y(k+1)).^4)-(2.^(2*k+1))*y(k+1)*(1+y(k+1)+y(k+1).^2);
end
vpa(1/a(n+1))