数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (1): 9-18.

• 论文 • 上一篇    下一篇

COMPARISON OF LAGRANGE INTERPOLATION AND HERMITE-FEJER TYPE INTERPOLATION OF HIGHER ORDER

史应光   

  1. Computing Center, Academia Sinica, PO Box 2719, Beijing 100080, China
  • 收稿日期:1991-03-04 出版日期:1994-03-25 发布日期:1994-03-25

COMPARISON OF LAGRANGE INTERPOLATION AND HERMITE-FEJER TYPE INTERPOLATION OF HIGHER ORDER

Shi Yingguang   

  1. Computing Center, Academia Sinica, PO Box 2719, Beijing 100080, China
  • Received:1991-03-04 Online:1994-03-25 Published:1994-03-25

PDF (PC)

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摘要： In this paper the following theorem (see[1, Problem 24 of P. Turan]) is given:If the Hermite-Fejer type interpolation process of order s ≥ 4, even, converges for any f ∈ Cs-2[-1, 1] then the Lagrange interpolation process defined on the same nodes converges for f' ∈Lipα with α > α0, where
α0=[((196s4-20s4-35s2+30s+9)(1)/2-(10s2+11s+3))]/[6s(2s+1)].

Abstract: In this paper the following theorem (see[1, Problem 24 of P. Turan]) is given:If the Hermite-Fejer type interpolation process of order s ≥ 4, even, converges for any f ∈ Cs-2[-1, 1] then the Lagrange interpolation process defined on the same nodes converges for f' ∈Lipα with α > α0, where
α0=[((196s4-20s4-35s2+30s+9)(1)/2-(10s2+11s+3))]/[6s(2s+1)].

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