✦ LIBER ✦

Uniform Convergence of Lagrange Interpolation Based on the Jacobi Nodes

✍ Scribed by George Kvernadze

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 485 KB
Volume: 87
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.0100

No coin nor oath required. For personal study only.

✦ Synopsis

Necessary and sufficient conditions are obtained for a continuous function guaranteeing the uniform convergence on the whole interval [ &1, 1] of its Lagrange interpolant based on the Jacobi nodes. The conditions are in terms of 4-variation, 8-variation, the modulus of variation, and the Banach indicatrix of a function.

1996 Academic Press, Inc.

n

(1)=( n+: n ), n # N. The system _( ) is defined uniquely and is called the Jacobi system of polynomials.

📜 SIMILAR VOLUMES

On Generalized Hermite–Fejér Interpolati

On Generalized Hermite–Fejér Interpolation of Lagrange Type on the Chebyshev Nodes

✍ Graeme J. Byrne; T.M. Mills; Simon J. Smith 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 131 KB

For f # C [&1, 1], let H m, n ( f, x) denote the (0, 1, ..., m) Hermite Feje r (HF) interpolation polynomial of f based on the Chebyshev nodes. That is, H m, n ( f, x) is the polynomial of least degree which interpolates f (x) and has its first m derivatives vanish at each of the zeros of the nth Ch

On the Order of Convergence of Simultane

On the Order of Convergence of Simultaneous Approximation by Lagrange-Hermite Interpolation

✍ Theodore Kilgore; Jürgen Prestin 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 307 KB

Convergence of Modified Lagrange Interpo

Convergence of Modified Lagrange Interpolation toLp-Functions Based on the Zeros of Orthonormal Polynomials with Freud Weights

✍ R. Sakai 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 204 KB

We consider the ``Freud weight'' W 2 Q (x)=exp( &Q(x)). let 1<p< , and let L\* n ( f ) be a modified Lagrange interpolation polynomial to a measurable , where 2 is a constant depending on p and :.