Spline Interpolation at Knot Averages on a Two-Sided Geometric Mesh

Odd-degree spline interpolation at a biinfinite knot sequence

one fundamental spline Li (i.e., Li(tj) = δij , all j), of order 2r whose rth derivative is square integrable. Further, L (r) i (x) is shown to decay exponentially as x moves away from ti, at a rate which can be bounded in terms of r alone. This allows one to bound odd-degree spline interpolation at knots on bounded functions in terms of the global mesh ratio Mt := supi,j ∆ti/∆tj . A very nice ...

Geometric Interpolation by Quartic Rational Spline Motions

We discuss piecewise rational motions with first order geometric continuity. In addition we describe an interpolation scheme generating rational spline motions of degree four matching given positions which are partially complemented by associated tangent information. As the main advantage of using geometric interpolation, it makes it possible to deal successfully with the unequal distribution o...

Two-sided averages for which oscillation fails

We show that in any invertible, ergodic, measure-preserving system, the two-sided square function obtained by comparing forward averages with their backwards counterparts, will diverge if the (time) length of the averages grows too slowly. This contrasts with the onesided case. We also show that for any sequence of times, certain weighted sums of the forward averages diverge. This contrasts wit...

Two-dimensional spline interpolation algorithms

Discrete Cubic Spline Interpolation over a Nonuniform Mesh

For i = 1,2, ••• ,n, pi shall denote the length of the mesh interval [xi-i,Xi\. Let p = m.sxi<i<npi and p' = mini<i<n p{. P is said to be a uniform mesh if pi is a constant for all i. Throughout, h will represent a given positive real number. Consider a real function s(x, h) defined over [a,6] which is such that its restriction Si on [XÌ-I,XÌ] is a polynomial of degree 3 or less for i = 1,2, • ...