CONVEXITY-PRESERVING PIECEWISE RATIONAL QUARTICINTERPOLATION

摘要

A family of piecewise rational quartic interpolants is given. Identified uniquely bythe value of a tension parameter Ai, each interpolant of the family can be C2 spline without solvinga linear or nonlinear system of consistency equations for the derivative values at the knots. Theinterpolant can preserve the local convexity/concavity properties of the given data. A proper choiceof Ai to guarantee shape preservation is given. A convergence analysis establishes an error boundin terms of Ai and shows that 0(h3) accuracy is obtained for C2 continuity. Several examples aresupplied to support the practical value of the method.