-1
$\begingroup$

Faber polynomials appear to be used to algorithmically approximate the complex exponential function $\exp(-ix)$ for example as in the case of the time evolution in quantum mechanics, for a Hermitian matrix $H$ and time $t$, an approximation to $\exp(-iHt)$ . In approximation theory, however it is very common to use, e.g., the Chebyshev polynomials in combination with a Taylor series approach to first take the Taylor series approximation to the exponential function, second truncate it, and then third approximate the monomials with a Chebyshev polynomial. Since I am very unfamiliar with the Faber polynomial approach, I was wondering whether there is a benefit using it and whether it gives better bounds for approximating the complex exponential?

$\endgroup$

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.