Constrained control and approximation properties of a rational interpolating curve

Authors:
Qi Duan;K. Djidjeli;W. G. Price;E. H. Twizell
Affiliations:
Department of Mathematics, Shandong University, PR China and School of Engineering Sciences, Ship Science, University of Southampton, Southampton and Department of Mathematical Sciences, Brunel Un ...;School of Engineering Sciences, Ship Science, University of Southampton, Southampton SO17 1BJ, UK;School of Engineering Sciences, Ship Science, University of Southampton, Southampton SO17 1BJ, UK;Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, UK
Venue:
Information Sciences: an International Journal
Year:
2003

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Abstract

This paper deals with the convexity control and the strain energy control of interpolating curves using a rational cubic spline with linear denominator. The sufficient and necessary conditions for controlling the interpolating curve to be convex or concave are derived. When the function being interpolated is f(t) ∈ C (3) [ t 0 , t n ], the error estimation of the interpolating function and the boundedness of the optimal error coefficient and its double symmetry with regard to parameters are obtained.