Abstract
A mathematical characterization of nonlinear interpolating spline curves is developed through a variational calculus approach, based on the Euler–Bernoulli large-deflection theory for the bending of thin beams or elastica. Algorithms previously proposed for computing discrete approximations of nonlinear interpolating splines are discussed and compared. The discrete natural cubic interpolating spline is discussed. An algorithm for computing discrete natural cubic splines is given and analyzed for discretization error and computational difficulty. Finally, a new algorithm and its FORTRAN implementation are given for computing discrete nonlinear spline functions.
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