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 | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-03-01594-1

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