hermite_interpolant, a MATLAB code which constructs the Hermite polynomial which interpolates function and derivative values at given points.
In other words, the user supplies n sets of data, (x(i),y(i),yp(i)), and the algorithm determines a polynomial p(x) such that, for 1 <= i <= n
p(x(i)) = y(i)
p'(x(i)) = yp(i)
Note that p(x) is a "global" polynomial, not a piecewise polynomial. Given n data points, p(x) will be a polynomial of degree 2n-1. As the value n increases, the increasing degree of the interpolating polynomial makes it liable to oscillations between the data, and eventually to severe inaccuracy even at the data points.
Generally, the interpolation problem for a large number of data points should be handled differently, for instance by piecewise polynomials.
The information on this web page is distributed under the MIT license.
hermite_interpolant is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version.
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