Wrong answer using " fft (ifft ( vector )) "

For my following vector when I use fft (ifft ( vector )) the answer is almost same as vector but at 129th position its different whereas the answer should be same as vector. Please help.

vector= 
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fft (ifft ( vector ))=
[7780728.00000002 + 0.00000000000000i
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Answer 1

[Andrew Newell]

The FFT algorithm is a numeric algorithm, with the inevitable round-off errors (see Floating point numbers), so you can't expect exact agreement.

Try the command

max(abs(vector-fft(ifft(vector))))

You'll find the maximum difference is about 1.8e-10.