Convergence of deficient quintic spline interpolation
by
P.R.S. Choudhary
Department of Mathematics, Government Autonomous-Science College, Jabalpur (M.P.) - 482001
Coauthors: S.S. Rana (Department of Mathematics and Computer Science. R.D. University, Jabalpur M.P. 482001)

In order to represent a non analytic function the most popular methods of piecewise polynomial approximation are piecewise linear interpolation and piecewise cubic interpolation. In the study of piecewise linear functions it is an advantage that some important properties like monotonicity and convexity are preserved but we get corners at the joints of two linear pieces and therefore to achieve a prescribed accuracy we require more data than some higher order method which is not a favourable and convenient situation. Considering a problem of spline interpolation Dikshit and Rana (Journal Approximation Theory, 45(1985), 350 - 357.) have shown the convergence properties of cubic spline for a wider choice of points of interpolation for a non uniform mesh. In the direction of more higher degree spline, Howell and Verma ( J. Approx. Theory 58 (1989), 58-67. ) have obtained optimal errors bounds for quartic interpolatory splines. Best error bounds for deficient quartic spline interpolation has been studied by Rana and Dubey ( Indian J. Pure Appl. Math. 30 (4): 385-393, 1999 ). In this paper, we have obtained best error bounds of deficient quintic spline interpolation matching the given functional values and spline at two intermediate points between the successive mesh points and also the second derivatives of spline and given function at mesh points with approximate boundary conditions.

key words:- Convergence, deficient, quintic spline, interpolation, Best Error Bounds.

Date received: August 7, 2003