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FOURFUN: A new system for automatic computations using Fourier expansions


Abstract Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
Created Date 2014-05
Contributor Mcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis Director) / Gelb, Anne (Committee Member) / Barrett, The Honors College / School of Mathematical and Statistical Sciences / School of International Letters and Cultures
Subject Matlab / Computational Mathematics / Fourier Series
Series Academic Year 2013-2014
Type Text
Extent 38 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS


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