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I'm an undergrad computer science student. As part of my calculus course I need to write a 'paper' (of course not as serious as a PhD paper) telling about a cool (for me) application of taylor/fourier series in software development or general computer science.

The only rule is 'not PI approximation'.

Any good ideas, I've made a research in EBSCO, ACM library and even IEEE but I can't find something useful to me.

Best regards!

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    Just to stave off any probable future comments: Taylor series are **not that commonly** used for the numerical evaluation of transcendental functions; since Taylor expansions are only really useful for evaluation near the expansion point, additional machinery is often needed to make them practical for a wider argument range, and even then, there are often better methods for the numerics. Nevertheless, they are a useful starting point.2012-05-08

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Here are some ideas:

  • The Schönhage-Strassen fast multiplication algorithm is based on FFT.
  • Media compression methods are based on variants of FFT. For example, JPEG is based on a two-dimensional version of a variant of FFT known as DCT.
  • In general, FFT is a basic tool in digital signal processing. It's use for example in speech recognition to extract the formants.
  • Algorithms for computing transcendental functions are sometimes based on Padé approximants, which are a generalization of Taylor series.
  • Algorithms used in CAS to calculate the asymptotics of general expressions use Taylor series.
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    I dont see how DCT cuts effort in half. Instead of computing a N complex DFT (N complex=2N scalars, half of them redundant because signal is real), DCT computes the 2N DFT of an mirrored (even) signal (which results in a 2N scalars -DFT is real- half of which are again redundant). There is no simplification, the cosine transform is just another unitary transform, they're basically equal in performance, and just equal in storage and precision (both have an exact inverse except for rounding noise), it's just that the DCT performs better than Fourier for compacting energy for typical images.2012-05-09