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For the Hermite interpolation polynomial, Hm(x) we prove for any function f ∈ C(2q)([−1, 1]) and ... more For the Hermite interpolation polynomial, Hm(x) we prove for any function f ∈ C(2q)([−1, 1]) and any s = 0, 1, 2, . . . , q, where q is a fixed integer that |H m (x) − f (x)| = O(1)ω( 1 m , f ) log n n2q−2s . Here m is defined by m = 3n− 1. If f ∈ C(q)([−1, 1]), then |H m − f (x)| = O(1)ω( 1 m , f ) log n (1 − x2)q/2 for x ∈ (−1, 1). 2000 Mathematics Subject Classification: 41A05.
Acta Mathematica Hungarica, 1987
Journal of Porous Media, 2015
For the Hermite interpolation polynomial, Hm(x) we prove for any function f ∈ C(2q)([−1, 1]) and ... more For the Hermite interpolation polynomial, Hm(x) we prove for any function f ∈ C(2q)([−1, 1]) and any s = 0, 1, 2, . . . , q, where q is a fixed integer that |H m (x) − f (x)| = O(1)ω( 1 m , f ) log n n2q−2s . Here m is defined by m = 3n− 1. If f ∈ C(q)([−1, 1]), then |H m − f (x)| = O(1)ω( 1 m , f ) log n (1 − x2)q/2 for x ∈ (−1, 1). 2000 Mathematics Subject Classification: 41A05.
Acta Mathematica Hungarica, 1987
Journal of Porous Media, 2015