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

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Bart Boesman 2014-8-6

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https://ww2.mathworks.cn/matlabcentral/answers/146553-cosine-sine-polynomial-summation-ordinary-sum-vs-clenshaw-summation

编辑： Bart Boesman 2014-8-6

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