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Cosine/Sine polynomial summation: Ordinary sum vs. Clenshaw summation

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Bart Boesman
Bart Boesman on 6 Aug 2014
Edited: Bart Boesman on 6 Aug 2014
Hi all,
I'm interested in knowing whether it is advantageous, specifically in matlab, to sum a cosine/sine polynomial using the clenshaw algorithm or not:
f(x) = sum_k=0:N a_k * cos kx or f(x) = sum_k=1:N a_k * sin kx
x can as well be a single value or an array of (arbitrarily chosen) values.
Many references advice to use special algorithms such as clenshaw summation in stead of simply summing harmonics of sines/cosines, however when implementing both, I don't see much difference both in computation time as accuracy. Tested it for max(N) = 60 at this moment.
Thanks in advance,
Bart

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