Asymptotics and Representation of Cubic Splines.
CALIFORNIA UNIV SAN DIEGO LA JOLLA
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The local asymptotic behavior of a cubic spline interpolator with equal bin size and its derivatives is determined to the first order precisely in the interior as the bin size tends to zero. It is shown that this asymptotic behavior is independent of the boundary conditions usually made use of in the case of spline interpolation on a finite interval. However, if the local behavior at the boundary or global asymptotic behavior is of interest, the type of boundary conditions assumed can determine what happens. Precise estimates of global asymptotic behavior are also derived. An explicit and simple representation is given for the cubic spline interpolator on the infinite line as well as the doubly cubic spline interpolator on the infinite plane.
- Numerical Mathematics