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Manuscript Title: An exponential spline interpolation for unequally spaced data points.
Authors: V. Tornow
Program title: LSPLIN
Catalogue identifier: AAOW_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 28(1982)61
Programming language: Fortran.
Computer: HP3000.
Operating system: HP3000 MPE IV, HB66/80 GCOS 4JS3.
RAM: 16K words
Word size: 16
Peripherals: graph plotter.
Keywords: General purpose, Interpolation, Spline, L-spline, Differentiation.
Classification: 4.10.

Nature of problem:
Quite often it is necessary to interpolate discrete points given in an interval (x1,xn) to some intermediate point x*epsilon(x1,xn) in such a way that one avoids spurious oscillations.

Solution method:
Instead of minimizing Sigma(i=1,N-1)Integral(xi,xi+1)[f(2)(x)]**2dx, where f is the interpolating function and f(k) is the kth derivative, we minimize the expression Sigma(i=1,N-1)Integral(xi,xi+1)[f(2)(x)]**2 + (lambda**2)i[f(1)(x)]**2dx with a weight parameter lambda i which indicates the relative importance of the first derivative of the interpolating function f in the minimization process.