Approximating the jump discontinuities of a function by its FourierJacobi coefficients
Author:
George Kvernadze
Journal:
Math. Comp. 73 (2004), 731751
MSC (2000):
Primary 65D99, 65T99, 42C10
Published electronically:
July 29, 2003
MathSciNet review:
2031403
Fulltext PDF Free Access
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Abstract: In the present paper we generalize Eckhoff's method, i.e., the method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its FourierChebyshev coefficients. A new method enables us to approximate the locations of discontinuities and the associated jumps of a discontinuous function, which belongs to a restricted class of the piecewise smooth functions, by means of its FourierJacobi coefficients for arbitrary indices. Approximations to the locations of discontinuities and the associated jumps are found as solutions of algebraic equations. It is shown as well that the locations of discontinuities and the associated jumps are recovered exactly for piecewise constant functions with a finite number of discontinuities. In addition, we study the accuracy of the approximations and present some numerical examples.
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Additional Information
George Kvernadze
Affiliation:
Department of Mathematics, Weber State University, Ogden, Utah 84408
Email:
gkvernadze@weber.edu
DOI:
http://dx.doi.org/10.1090/S0025571803015941
PII:
S 00255718(03)015941
Keywords:
Approximating the jump discontinuities,
FourierJacobi coefficients
Received by editor(s):
November 30, 2001
Received by editor(s) in revised form:
November 21, 2002
Published electronically:
July 29, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
