Alternatives to the exponential spline in tension

Pruess, Steven

doi:10.1090/S0025-5718-1979-0537971-6

Alternatives to the exponential spline in tension
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Math. Comp. 33 (1979), 1273-1281 Request permission

Abstract:

A general setting is given for smooth interpolating splines depending on a parameter such that as this parameter approaches infinity the spline converges to the piecewise linear interpolant. The theory includes the standard exponential spline in tension, a rational spline, and several cubic splines. An algorithm is given for one of the cubics; the parameter for this example controls the spacing of new knots which are introduced.

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