单调及保凸二次样条插值

本文将集中研究保形二次样条插值.假设序列X={x_i}和Y={y_i}(i=0,1,2,…,N)满足x_(i-1)

MONOTONE AND CONVEX QUADRATIC SPLINE INTERPOLATION

In this paper the necessary and sufficient condition for the existence of monotone qua-tratic interpolating spline is obtained, and then the problem proposed and studied by E.Passow is solved. A necessary and sufficient condition for the existence of monotone andconvex quadratic interpolatory spline is also established, and it is proved that such a condi-tion is equivalent to the one on 1/1 -algorithm given by F. McAllister, E. Passow and J. A.Roulier.