Why are these sums not the same?

Hello together,

What is the difference between these two:

1:

            >>sum(cos(0.5*pi)*(0:99))
            ans =

                3.0310e-13

and 2:

            >>S=0;
            >> for J=0:99
                S=cos(0.5*pi)*j;
               end;

            >> S =

               6.0620e-15

Why is there a different result?

Thank you for any help!

Answer 1

[Roger Stafford]

There is no reason they should be the same! In the for-loop method you are not doing a summation, as is done in the first method. All you obtain is the value of the last term, namely cos(0.5*pi)*99.

If you change the last method to

   S = S + cos(0.5*pi)*j;

any difference between that value and the one for the first method will be due to differences in round off errors.

Ideally cos(0.5*pi) should be an exact zero, but both because pi cannot be represented exactly and because of errors in the cosine computation, it actually gives 6.1232e-17 as its value.

Answer 2

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F