|MATLAB Function Reference|
Piecewise Cubic Hermite Interpolating Polynomial (PCHIP)
yi = pchip(x,y,xi)
yi containing elements corresponding to the elements of
xi and determined by piecewise cubic interpolation within vectors
y. The vector
x specifies the points at which the data
y is given. If
y is a matrix, then the interpolation is performed for each column of
pp = pchip(x,y)
returns a piecewise polynomial structure for use by
x can be a row or column vector.
y is a row or column vector of the same length as
x, or a matrix with
pchip finds values of an underlying interpolating function at intermediate points, such that:
spline constructs in almost the same way
pchip constructs . However,
spline chooses the slopes at the differently, namely to make even continuous. This has the following effects:
splineproduces a smoother result, i.e. is continuous.
splineproduces a more accurate result if the data consists of values of a smooth function.
pchiphas no overshoots and less oscillation if the data are not smooth.
pchipis less expensive to set up.
 Fritsch, F. N. and R. E. Carlson, "Monotone Piecewise Cubic Interpolation," SIAM J. Numerical Analysis, Vol. 17, 1980, pp.238-246.
 Kahaner, David, Cleve Moler, Stephen Nash, Numerical Methods and Software, Prentice Hall, 1988.