Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Accurate and efficient reconstruction of discontinuous functions from truncated series expansions


Author: Knut S. Eckhoff
Journal: Math. Comp. 61 (1993), 745-763
MSC: Primary 65T20; Secondary 65D10
DOI: https://doi.org/10.1090/S0025-5718-1993-1195430-1
MathSciNet review: 1195430
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Knowledge of a truncated Fourier series expansion for a discontinuous $ 2\pi $-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval $ [-1, 1]$, is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree M for the M locations of discontinuities in each period for a periodic function, or in the interval $ (-1, 1)$ for a nonperiodic function, is constructed. The M coefficients in that algebraic equation of degree M are obtained by solving a linear algebraic system of equations determined by the coefficients in the known truncated expansion. By solving an additional linear algebraic system for the M jumps of the function at the calculated discontinuity locations, we are able to reconstruct the discontinuous function as a linear combination of step functions and a continuous function.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65T20, 65D10

Retrieve articles in all journals with MSC: 65T20, 65D10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1993-1195430-1
Article copyright: © Copyright 1993 American Mathematical Society