학술논문
The three-term recursion for Chebyshev polynomials is mixed forward-backward stable.
Document Type
Article
Source
Subject
*CHEBYSHEV polynomials
*ERROR analysis in mathematics
*CHEBYSHEV systems
*POLYNOMIALS
*MATHEMATICAL bounds
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Language
ISSN
1017-1398
Abstract
This paper provides an error analysis of the three-term recurrence relation (TTRR) T( x)=2 x T( x)− T( x) for the evaluation of the Chebyshev polynomial of the first kind T( x) in the interval [−1,1]. We prove that the computed value of T( x) from this recurrence is very close to the exact value of the Chebyshev polynomial T of a slightly perturbed value of x. The lower and upper bounds for the function $C_{N}(x)= |T_{N}(x)| + |x T_{N}^{\prime }(x)|$ are also derived. Numerical examples that illustrate our theoretical results are given. [ABSTRACT FROM AUTHOR]