Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geome...

We discuss piecewise rational motions with first order geometric continuity. In addition we describe an interpolation scheme generating rational spline motions of degree four matching given positions which are partially complemented by associated tangent information. As the main advantage of using geometric interpolation, it makes it possible to deal successfully with the unequal distribution o...

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...

In this paper, Semi-orthogonal (SO) B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of linear and non-linear second order Fredholm integro-differential equations. The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this functions are presented to reduce the solution of linear and...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

Abstract: The aim of study is to solve parabolic integro-differential equation with a weakly singular kernel. Problems involving partial integro-differential equations arise in fluid dynamics, viscoelasticity, engineering, mathematical biology, financial mathematics and other areas. Many mathematical formulations of physical phenomena contain integro-differential equations. Integro-differential...

Deboor, C. , A Practical Guide to splines, Applied Mathematical Science, Vol. 27 Springer Verlag, New York, 1979. Hall, C. A. and Meyer, W. W. , J. Approximation Theory, 16(1976), pp. 105-122. Howel, G. and Verma, A. K. , Best Error Bond of Quartic Spline Interpolation, J. Appron Theory 58 (1989), 58-67. Davis, P. J. , Interpolation and approximation. New Yrok, 1961. Agrawal, R. P. and Wong, P....

The problem of C interpolation of a discrete set of data on the interval [a,b] representing the function f using quartic splines is investigated. An explicit scheme of interpolation is obtained using different quartic splines on even and odd subintervals of interpolation. Mathematical Subject Classification: 41A05, 41A15