Automatic tension adjustment for interpolatory splines

The authors deal with anomalous oscillations often exhibited by cubic spline interpolating curves. These oscillations, which are not suggested by the data, can be treated with a shaping parameter called tension, which is introduced by generalizing the cubic spline formation in some fashion. The authors consider the associated problem of estimating the magnitude of the tensions necessary to achieve a desired shape. The analysis is based on a theory they reported earlier, called convexity interval analysis, and it leads to an algorithm that produces suitable tension values for given data automatically, without experimentation or interactive user direction. Three examples are given to illustrate the concepts.<>