Interpolatory tension splines with automatic selection of tension factors
SIAM Journal on Scientific and Statistical Computing
Exact equations of the nonlinear spline
ACM Transactions on Mathematical Software (TOMS)
Minimal surfaces and Sobolev gradients
SIAM Journal on Scientific Computing
Unified representations of nonlinear splines
Journal of Approximation Theory
ACM Transactions on Mathematical Software (TOMS)
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We describe a new method and a Fortran-77 code for constructing discrete approximations to nonparametric interpolating nonlinear spline curves. Our approach consists of minimizing the discretized strain energy by a descent method with a Sobolev gradient in place of the standard gradient. It serves as a demonstration of the Sobolev gradient method, which is much more generally applicable. The effectiveness of the method in rapidly producing smooth interpolatory curves is demonstrated by test results for several challenging data sets.