1 research outputs found
On improving the accuracy of Horner's and Goertzel's algorithms
It is known that Goertzel's algorithm is much less numerically accurate than
the Fast Fourier Transform (FFT)(Cf. \cite{gen:69}). In order to improve
accuracy we propose modifications of both Goertzel's and Horner's algorithms
based on the divide-and-conquer techniques. The proof of the numerical
stability of these two modified algorithms is given. The numerical tests in
Matlab demonstrate the computational advantages of the proposed modifications.
The appendix contains the proof of numerical stability of Goertzel's algorithm
of polynomial evaluation.Comment: 22 pages, 3 figures, presented on the GAMM Meeting, Brunschweig,
September 200