Accurate Goertzel Algorithm: Error Analysis, Validations and Applications

The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be less expensive than the other special cases. In this paper, we present a new compensated algorithm to improve accuracy by using error-free transformations. We derive forward round-off error bound for our algorithm, which implies that yields full precision polynomials not too ill-conditioned. A dynamic estimate is also presented running analysis. Moreover, show cases evaluating polynomials. Numerical experiments indicate run faster those while producing same accurate results, absolutely stable when condition number smaller 1016. An application given illustrate more MATLAB’s fft function. results relative from 1015 1017, was 1012 1015.