How to stop the loop when percentage error is reached?

It is known that the values of the following three sums, accurate to 12 decimal places, are:

For each k, the objective of this problem is to determine N so that the approximate value of the sum is such that the relative percentile error is less than or equal to 0.025%

In the main script input the value of k = 3; 5; or 7.

Depending on the value of k, evaluate the exact sum S and call the function sumserf(k,S) which should return the approximate value of the sum, the relative error, and the value of N needed to meet the above percentile accuracy. If you input k that is not 3, 5, or 7, the script should display an error message and ask you to input a correct value of k.

You should also use a while loop which allows you to input different values of k during one run of the code.

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The output should look like this:

Enter the exponent k:2

ERROR: You entered incorrect k. Possible choices are: 3, 5, and 7

Enter the exponent k:3

Sum for k = 3, exact sum = 1.20206, approx sum = 1.20177 for N = 41

rel percent error = 0.024

Do you want another k: Yes (1) or No (0)

1

Enter the exponent k:5

Sum for k = 5, exact sum = 1.03693, approx sum = 1.03679 for N = 6

rel percent error = 0.013

Do you want another k: Yes (1) or No (0)

1

Enter the exponent k:7

Sum for k = 7, exact sum = 1.00835, approx sum = 1.00827 for N = 3

rel percent error = 0.008

Do you want another k: Yes (1) or No (0)

0

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 while(1)

    k=input('Enter the exponent '); 

    if(k==3)

        sumSerf(k,1.202056903150) 

        fprintf('Sum for k = %d, exact sum = %.5f, approx sum = %.5f for N = %d', k, S, sum, n)

        fprintf('rel percent error = %.3f', error)

    elseif(k==5)

        sumSerf(k,1.036927755143)

        fprintf('Sum for k = %d, exact sum = %.5f, approx sum = %.5f for N = %d', k, S, sum, n)

        fprintf('rel percent error = %.3f', error)

    elseif(k==7)

        sumSerf(k,1.008349277382)

        fprintf('Sum for k = %d, exact sum = %.5f, approx sum = %.5f for N = %d', k, S, sum, n)

        fprintf('rel percent error = %.3f', error)

    else

        fprintf('ERROR: You entered incorrect k. Possible choices are: 3, 5, and 7\n') 

    end

    c=input('Do you want another k: Yes (1) or No (0)');

    if(c==0)

        break

        end

    end

and here's the function:

function [sum,n,error] = sumSerf(k,S)

error=1;

sum=1;

n=1;

i=2;

while(error>=0.025*abs(sum-S)/sum)

sum=sum+(1/ power(i,k));

n=n+1;

i=i+1;

end

error=0.025*abs(sum-S)/sum;

end

When I tested it, it just keep looping without giving an answer. How to stop the loop? Is there anything I did wrong that need to be fixed?

Answer 1

[KSSV]

Check the below pseudo code..to exit a loop if condition is met:

N = 100 ;

for i = 1:N
    x = rand ;
    if x<0.1
        fprintf('Condition met: exititng the loop; iterations:%d\n',i)
        break
    end
end

[Ariel Chou]

Do I put it at the end of my function? (within the while loop or outside the while loop?)

[KSSV]

It is an example code on how to exit loop when a condition is met......understand it and implement it in your code.