TY - JOUR
AU - Milovanović, G.V.
AU - Orive, R.
AU - Spalević, M.M.
T1 - Quadratures with multiple nodes for Fourier-Chebyshev coefficients
LA - eng
PY - 2019
SP - 271
EP - 296
T2 - IMA Journal of Numerical Analysis
SN - 1464-3642
VL - 39
IS - 1
PB - Oxford University Press
AB - Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanović & Spalević (2014, Math. Comput., 83, 1207-1231).
DO - 10.1093/IMANUM/DRX067
UR - https://portalciencia.ull.es/documentos/5e3c3f6f29995246bbf61759
DP - Dialnet - Portal de la Investigación
ER -