Write a Matlab script that inputs a small number ε and large positive integer nMax, computes the smallest n∗such that

Question

Jason 2022-9-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1811875-write-a-matlab-script-that-inputs-a-small-number-and-large-positive-integer-nmax-computes-the-sma

回答： Geoff Hayes 2022-9-25

So this question uses a while loop, and I almost have the correct answer, I just don't know how to input the maximum nMax into the while loop. This is what I have so far. When ep=10^-3 and nMax=10^3, it should display that n*=22 and fn_star=0.0217357060868536

%smallest n number
ep=input('Enter smal number epsilon:');
f=n*(1-cos(1/n));
fn=(n+1)*(1-cos(1/n));
err=abs(f-fn);
while err>=ep
    n=n+1;
    nMax=input('Enter maximum:');
    f=fn;
    fn=(n+1)*(1-cos(1/n));
    err=abs(f-fn);
end
ns=n;
fprintf('for epsilon=%.16e\n',ep)
fprintf('the smallest value n*=%.16d\n',ns)
fprintf('fn_star=%.16f\n',fn)

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Answer 1

Geoff Hayes 2022-9-25

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@Jason - I think you just need to get the nMax outside of the loop as presumably it is used to set a maximum number of iterations for the loop. For example,

ep=input('Enter smal number epsilon:');
nMax=input('Enter maximum:');
f=n*(1-cos(1/n));
fn=(n+1)*(1-cos(1/n));
err=abs(f-fn);
while err>=ep && n <= nMax
    n=n+1;
    f=fn;
    fn=(n+1)*(1-cos(1/n));
    err=abs(f-fn);
end