Explicit error estimates for quintic and biquintic spline interpolation

AbstractWe obtain explicit error estimates between a given function f ϵ C(n)[a, b], 2 ⩽ n ⩽ 6 and its quintic Hermite and spline interpolates. These results are then used to obtain definite error estimates between a given function f ϵ C(n,n)([a, b] × [c, d]) and its biquintic spline interpolate. Sufficient numerical illustration which dwells upon the sharpness of the obtained inequalities is also included