Panagiotis S. Vigklas

Advances on the continued fractions method using better estimations of positive root bounds

We present an implementation of the Continued Fractions (CF) real root isolation method using a recently developed upper bound on the positive values of the roots of polynomials. Empirical results presented in this paper verify that this implementation makes the CF method always faster than the Vincent-Collins-Akritas bisection method, or any of its variants.

SOLVING THE HEAT AND WAVE EQUATIONS WITH THE (FAST) DISCRETE FOURIER TRANSFORM

Motivated by the excellent work of Bill Davis and Jerry Uhl “Differential Equations & Mathematica” [2], we present in detail a little known application of the fast Discrete Fourier Transform (DFT), also known as FFT. Namely, we first examine the use of FFT in approximating polynomials with sines and cosines (also known as Fast Fourier Fit or FFF) and then derive the heat and wave equations. This presentation is ideally suited for educational purposes.