Strong asymptotics in Lagrange interpolation with equidistant nodes

✍ Scribed by Michael I. Ganzburg

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 200 KB
• Volume: 122
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(03)00070-4

✦ Synopsis

In this paper we prove three conjectures of Revers on Lagrange interpolation for f l ðtÞ ¼ jtj l ; l40; at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants L N ð f l ; tÞ for 0ojtjo1; and discuss their convergence at t ¼ 0: We also establish an asymptotic relation for max jtjp1 j jtj l À L N ð f l ; tÞj: The proofs are based on strong asymptotics for jtj l À L N ð f l ; tÞ; 0pjtjo1: