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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Approximating the jump discontinuities of a function by its Fourier-Jacobi coefficients


Author: George Kvernadze
Journal: Math. Comp. 73 (2004), 731-751
MSC (2000): Primary 65D99, 65T99, 42C10
Published electronically: July 29, 2003
MathSciNet review: 2031403
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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 Fourier-Chebyshev 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 Fourier-Jacobi 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/S0025-5718-03-01594-1
PII: S 0025-5718(03)01594-1
Keywords: Approximating the jump discontinuities, Fourier-Jacobi 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