Sharp error bounds for Jacobi expansions and Gegenbauer--Gauss quadrature of analytic functions

• Main Authors: Zhao, Xiaodan, Wang, Li-Lian, Xie, Ziqing
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
• Online Access: https://hdl.handle.net/10356/101170; http://hdl.handle.net/10220/18308
• Institution: Nanyang Technological University

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expa...