Blends have decent numerical properties

نویسندگان

چکیده

A "blend" is a two-point Hermite interpolational polynomial, typically of quite high degree. This note shows that implementing them in double Horner evaluation scheme has good backward error, and also the Lebesgue constant for balanced blend or nearly on interval [0,1] bounded by 2, independently grade degree approximation. On [-1,1], which more natural comparison, it course unbounded, but grows only like 2√(m/π) where 2m+1 I show quadrature schemes blends amplify errors O( ln(m) ).

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ژورنال

عنوان ژورنال: Maple transactions

سال: 2023

ISSN: ['2564-3029']

DOI: https://doi.org/10.5206/mt.v3i1.15890