4.5.41 Problem

Suppose that fk4(a,b) and SΔ(x) are spline interpolating functions that interpolate node points Δ={a=x0<x1<<xn=b}. Show that:


if only one of the following conditions is satisfied:

  1. f(x)=SΔ(x)x=a,b

  2. f(x)=SΔ(x)x=a,b

  3. fkp4(a,b),periodicSΔ



If we apply integration by parts twice on each of above integrals, we will have:


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