On the Lebesgue constant of Berrut’s rational interpolant at equidistant nodes

نویسندگان

  • Len Bos
  • Stefano De Marchi
  • Kai Hormann
چکیده

We study the Lebesgue constant of the rational interpolant of Berrut (cf. [1]) when the interpolation points are equally distributed. In the more general case of the rational interpolant of Floater and Hormann (cf. [6]), we show by several numerical results, that the behavior of the Lebesgue constant on equally distributed points is consistent with that of Berrut’s interpolant.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bounding the Lebesgue constant for Berrut's rational interpolant at general nodes

It has recently been shown that the Lebesgue constant for Berrut’s rational interpolant at equidistant nodes grows logarithmically in the number of interpolation nodes. In this paper we show that the same holds for a very general class of well-spaced nodes and essentially any distribution of nodes that satisfy a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as ex...

متن کامل

A tighter upper bound on the Lebesgue constant of Berrut's rational interpolant at equidistant nodes

It is well known that polynomial interpolation at equidistant nodes can give bad approximation results and that rational interpolation is a promising alternative in this setting. In this paper we confirm this observation by proving that the Lebesgue constant of Berrut’s rational interpolant grows only logarithmically in the number of interpolation nodes. Moreover, the numerical results show tha...

متن کامل

On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and importan...

متن کامل

Barycentric rational interpolation at quasi-equidistant nodes

A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes. But ...

متن کامل

On the Lebesgue constant for Lagrange interpolation on equidistant nodes

Properties of the Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that the Lebesgue function can be formulated both in terms of a hypergeometric function 2F1 and Jacobi polynomials. Moreover an integral expression of the Lebesgue function is also obtained. Finally, the asymptotic behavior of the Lebesgue constant is studied.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010