Error estimates for discrete spline interpolation: Quintic and biquintic splines

In this paper we shall develop a class of discrete spline interpolates in one and two independent variables. Further, explicit error bounds in ? ∞ norm are derived for the quintic and biquintic discrete spline interpolates. We also present some numerical examples to illustrate the results obtained.

[1]  Ravi P. Agarwal,et al.  Sharp error bounds for the derivatives of Lidstone-spline interpolation II , 1994 .

[2]  Riaz A. Usmani.  Applied Linear Algebra , 1986 .

[3]  R. Agarwal,et al.  Error Inequalities for Discrete Hermite and Spline Interpolation , 1998 .

[4]  R. Usmani.  On quadratic spline interpolation , 1987 .

[5]  Fengmin Chen,et al.  Solutions of Fredholm integral equations via discrete biquintic splines , 2013, Math. Comput. Model..

[6]  Xuli Han,et al.  A degree by degree recursive construction of Hermite spline interpolants , 2009 .

[7]  B. Garay,et al.  Discretization of semilinear differential equations with an exponential dichotomy , 1994 .

[8]  Tom Lyche,et al.  Discrete polynomial spline approximation methods , 1976 .

[9]  Ravi P. Agarwal,et al.  Error Inequalities in Polynomial Interpolation and their Applications , 1993 .

[10]  L. Schumaker,et al.  Best Summation Formulae and Discrete Splines , 1973 .

[11]  A. Kouibia,et al.  Approximation by interpolating variational splines , 2008 .

[12]  A. K. Pani,et al.  Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation , 2005 .

[13]  Ravi P. Agarwal,et al.  Explicit error estimates for Quintic and biquintic spline interpolation II , 1994 .

[14]  Explicit error bounds for the derivatives of spline interpolation in L2 norm , 1994 .

[15]  T. Lyche.  Discrete cubic spline interpolation , 1976 .

[16]  L. Schumaker,et al.  DISCRETE SPLINES VIA MATHEMATICAL PROGRAMMING. , 1971 .

[17]  Fengmin Chen,et al.  Error inequalities for quintic and biquintic discrete Hermite interpolation , 2011, J. Comput. Appl. Math..

[18]  DiscreteL-splines , 1974 .

[19]  Quintic spline solutions of fredholm integral equations of the second kind , 1990 .