Deficient quartic spline of Marsden type with minimal deviation by the data polygon

摘要

In this work we construct the deficient quartic spline with the knots following the Marsden's scheme and prove the existence and uniqueness of the deficient quartic spline with minimal deviation by the data polygon. The inter-polation error estimate of the obtained quartic spline is given in terms of the modulus of continuity. A numerical example is included in order to illustrate the geometrical behaviour of the quartic spline with minimal quadratic oscillation in average in comparison with the two times continuous differentiable deficient quartic spline.