Error bounds in periodic quartic spline interpolation

In this paper we develop periodic quartic spline inter polation theory which, in general, gives better fits to continuous functions than does the existing quintic spline inter polation theory. The main theorem of the paper is to establish that ⋎s^(r)-y^(r)⋎=O(h^6−r), r=0,1,2,3. Also, the nonperiodic cases cannot be constructed empolying the methodology of this paper because that will involve several other end conditions entirely different than (1.10).