Uniform approximation by some Hermite interpolating splines

AbstractIn this paper some upper bound for the error ∥ s-f ∥∞ is given, where f ε C1[a,b], but s is a so-called Hermite spline interpolant (HSI) of degree 2q −1 such that f(xi) = s(xi), f′(rmxi) = s′(xi), s(j) (xi) = 0 (i = 0, 1, …, n; j = 2, 3, …, q −1; n > 0, q > 0) and the knots xi are such that a = x0 < x1 < … < xn = b. Necessary and sufficient conditions for the existence of convex HSI are given and upper error bound for approximation of the function fε C1[a, b] by convex HSI is also given