Linear barycentric rational quadrature
نویسندگان
چکیده
منابع مشابه
The Linear Barycentric Rational Quadrature Method for Volterra Integral Equations
We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate, but is costly on long integration intervals. The second, based on a composite version of the rational...
متن کاملThe Linear Barycentric Rational Quadrature Method for Volterra
We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a co...
متن کاملRecent advances in linear barycentric rational interpolation
Well-conditioned, stable and infinitely smooth interpolation in arbitrary nodes is by no means a trivial task, even in the univariate setting considered here; already the most important case, equispaced points, is not obvious. Certain approaches have nevertheless experienced significant developments in the last decades. In this paper we review one of them, linear barycentric rational interpolat...
متن کاملLinear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants
Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a s...
متن کاملConvergence of Linear Barycentric Rational Interpolation for Analytic Functions
Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly conditioned, these interpolants fail to converge even in exact arithmetic in some cases. Linear barycentric rational interpolation with the weights presented by Floater and Hormann can be viewed as blended p...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2011
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-011-0357-x