scholarly journals Convergence of Hermite–Fejér type interpolation of higher order on an arbitrary system of nodes

2003 ◽  
Vol 123 (2) ◽  
pp. 173-187
Author(s):  
Ying Guang Shi
Keyword(s):  
Higher Order ◽  
Arbitrary System ◽  
Type Interpolation

scholarly journals On Hermite-Fejér type interpolation

1983 ◽  
Vol 28 (1) ◽  
pp. 39-51 ◽  
Author(s):  
H.-B. Knoop ◽  
B. Stockenberg
Keyword(s):  
Jacobi Polynomial ◽  
Higher Order ◽  
Interpolation Operator ◽  
Type Interpolation

For the Hermite-Fejér interpolation operator of higher order constructed on the roots , 1 ≤ k ≤ m, of the Jacobi-polynomial it is shown that is positive for all m ∈ N, if (α, β) ∈ [−¾, −¼]2. Further there is given an bound, which implies for arbitrary f ∈ C(I) and (α, β) ∈ [−¾, −¼]2.

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