Volume 11, Issue 1
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On Some Applications of the Fast Discrete Fourier Transform
Motivated by the excellent work of Bill Davis and Jerry Uhl's Differential Equations & Mathematica [1], we present in detail several little-known applications of the fast discrete Fourier transform (DFT), also known as FFT. Namely, we first examine the use of the FFT in multiplying univariate polynomials and integers and approximating polynomials with sines and cosines (also known as the fast Fourier fit or FFF). We then examine the use of the FFF in solving differential equations with Laplace transforms and rediscovering trigonometric identities. | About the Authors
Alkiviadis G. Akritas taught at the University of Kansas for twenty years before he moved to Greece, where he has been teaching and doing research in the Department of Computer and Communication Engineering at the University of Thessaly, in Volos, since 1998. His research interests are in the field of symbolic and algebraic computations (a field in which he has published extensively) and in using computer algebra systems to improve the teaching of mathematics. Based on Vincent's theorem of 1836, Akritas has developed the two fastest methods for isolating the real roots of polynomial equations; these methods have been incorporated, respectively, in the computer algebra systems Maple and Mathematica. Jerry Uhl is a professor of mathematics at the University of Illinois at Urbana-Champaign. He is the author or coauthor of a number of research papers. During the 1980s, Uhl served as real analysis editor of the research journal Proceedings of the American Mathematical Society. He also served one term as managing editor of the same journal, as well as one term on the Council of the American Mathematical Society. Since 1988, Uhl has devoted nearly all his energies to Calculus&Mathematica. In 1998, he received an award for distinguished teaching from the Mathematical Association of America. Panagiotis S. Vigklas is a Ph.D. student in the Department of Computer and Communication Engineering at the University of Thessaly, in Volos. He is currently working on his dissertation under the supervision of A. G. Akritas. Alkiviadis G. Akritas University of Thessaly Department of Computer and Communication Engineering 37 Glavani & 28th October GR-38221, Volos Greece akritas@uth.gr inf-server.inf.uth.gr/~akritas/index.html Jerry Uhl University of Illinois at Urbana-Champaign Department of Mathematics 273 Altgeld Hall (mc 382) 1409 W. Green Urbana, IL 61801 USA juhl@cm.math.uiuc.edu Panagiotis S. Vigklas University of Thessaly Department of Computer and Communication Engineering 37 Glavani & 28th October GR-38221, Volos Greece pviglas@uth.gr |
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