Best error bounds for splines of degree six
by
Y.P. Dubey
535, Garha Bazar, Jabalpur (M.P.) India 482001
Coauthors: S. S. Rana (Department of Mathematics and Computer Science. Rani Durgavati University, Jabalpur M.P. 482001)

Piecewise linear and cubic interpolation are widely used schemes for piecewise Polynomial approximation. But such piecewise linear functions have corners at the joints of two linear pieces and therefore to achieve a prescribed accuracy usually more data are required than higher order method. Rana (Rocky Mountain Journal of Math., 18 (1988), 825-835), has studied the convergence properties of deficient cubic spline interpolation matching given functional value and derivative at interior points. The best error bounds for quartic spline interpolation has obtained by Howell and Verma ( J. Approx. Theory, 58 (1989), 58-67) . Tarazi and Sallam (Computing, 38(1987), 355-361) presented a formulation and studied a problem of quartic spline interpolation which can be applied to quadratures. Fawzy (Acta Math , Acad. Sci. , Hungar) and Fawzy and Holail (Jour. Approx. Theory, 49(1987), 110-114) suggested several local methods for solving lacunary interpolation problems using piecewise polynomials with certain continuity properties . In the present paper, we construct a spline method for solving a interpolation problem using piecewise polynomials of degree 6 which agree with the given function and its derivative at knots and function at mid points with appropriate boundary conditions. We also estimate the best error bound for the interpolant.

Key Words : Best Error Bounds, Spline and Interpolation.

Date received: August 7, 2003