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Approximating the jump discontinuities of a function by its Fourier-Jacobi coefficients
Author(s):
George
Kvernadze.
Journal:
Math. Comp.
73
(2004),
731-751.
MSC (2000):
Primary 65D99, 65T99, 42C10
Posted:
July 29, 2003
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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:
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
Posted:
July 29, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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