A Chebyshev Quadrature Rule for One Sided Finite Part Integrals

Philsu Kim

doi:10.1006/jath.2001.3572

A Chebyshev Quadrature Rule for One Sided Finite Part Integrals

Philsu Kim

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Abstract

This paper is concerned with a Chebyshev quadrature rule for approximating one sided finite part integrals with smooth density functions. Our quadrature rule is based on the Chebyshev interpolation polynomial with the zeros of the Chebyshev polynomial T_N+1(τ)-T_N-1(t). We analyze the stability and the convergence for the quadrature rule with a differentiable function. Also we show that the quadrature rule has an exponential convergence when the density function is analytic.

Original language	English
Pages (from-to)	196-219
Number of pages	24
Journal	Journal of Approximation Theory
Volume	111
Issue number	2
DOIs	https://doi.org/10.1006/jath.2001.3572
State	Published - Aug 2001

Keywords

Chebyshev interpolation
Finite part integrals

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10.1006/jath.2001.3572

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abstract = "This paper is concerned with a Chebyshev quadrature rule for approximating one sided finite part integrals with smooth density functions. Our quadrature rule is based on the Chebyshev interpolation polynomial with the zeros of the Chebyshev polynomial TN+1(τ)-TN-1(t). We analyze the stability and the convergence for the quadrature rule with a differentiable function. Also we show that the quadrature rule has an exponential convergence when the density function is analytic.",

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AB - This paper is concerned with a Chebyshev quadrature rule for approximating one sided finite part integrals with smooth density functions. Our quadrature rule is based on the Chebyshev interpolation polynomial with the zeros of the Chebyshev polynomial TN+1(τ)-TN-1(t). We analyze the stability and the convergence for the quadrature rule with a differentiable function. Also we show that the quadrature rule has an exponential convergence when the density function is analytic.

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KW - Finite part integrals

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A Chebyshev Quadrature Rule for One Sided Finite Part Integrals

Abstract

Keywords

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