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Hermite interpolation - Cornell University

Bindel, Spring 2012 Intro to Scientific Computing (CS 3220)Week 10: Monday, Apr 2 Hermite interpolationFor standard polynomial interpolation problems, we seek to satisfy conditionsof the formp(xj) =yj,whereyjis frequently a sampled function valuef(xj). If all we know isfunction values, this is a reasonable approach. But sometimes we have constructs an interpolant based not onlyon equations for the function values, but also for the example, consider the important special case of finding a cubic poly-nomial that satisfies proscribed conditions on the values and derivatives atthe endpoints of the interval [ 1,1].

In addition to spline conditions, one can choose piecewise cubic polyno-mials that satisfy Hermite interpolation conditions (sometimes referred to by the acronym PCHIP or Piecewise Cubic Hermite Interpolating Polynomials). That is, the function values and derivatives are speci ed at each nodal point.

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