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Journal of Scientific Computing

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01-08-2014

Nonperiodic Trigonometric Polynomial Approximation

Author: Hillel Tal-Ezer

Published in: Journal of Scientific Computing | Issue 2/2014

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Abstract

The most common approach for approximating non-periodic function defined on a finite interval is based on considering polynomials as basis functions. In this paper we will address the non-optimallity of polynomial approximation and suggest to switch from powers of \(x\) to powers of \(\sin (px)\) where \(p\) is a parameter which depends on the dimension of the approximating subspace. The new set does not suffer from the drawbacks of polynomial approximation and by using them one can approximate analytic functions with spectral accuracy. An important application of the new basis functions is related to numerical integration. A quadrature based on these functions results in higher accuracy compared to Legendre quadrature.

previous article Optimal Strong-Stability-Preserving Runge–Kutta Time Discretizations for Discontinuous Galerkin Methods

next article A Class of Incomplete Riemann Solvers Based on Uniform Rational Approximations to the Absolute Value Function

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Title: Nonperiodic Trigonometric Polynomial Approximation
Author: Hillel Tal-Ezer
Publication date: 01-08-2014
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2014
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9797-6

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