TY - JOUR
A2 - Barrio, Roberto
AU - Yun, Beong In
PY - 2017
DA - 2017/11/22
TI - Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function
SP - 1364914
VL - 2017
AB - We introduce a generalized sigmoidal transformation wm(r;x) on a given interval [a,b] with a threshold at x=r∈(a,b). Using wm(r;x), we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.
SN - 1085-3375
UR - https://doi.org/10.1155/2017/1364914
DO - 10.1155/2017/1364914
JF - Abstract and Applied Analysis
PB - Hindawi
KW -
ER -