Jean Savoie

Periodic even degree spline interpolation on a uniform partition

Abstract Periodic even degree spline interpolants of a function f at the knots are considered. Existence and uniqueness results are proved, and error bounds of the form ∥ f k − s k ∥ ∞ ⩽ σ r , k h 2 r + 1 − k {∥ f (2 r + 1) ∥ ∞ + Var( f 2 r + 1) } ( k = 0,…, 2 r ) are obtained.

Periodic quadratic spline interpolation

On definit une fonction spline quadratique periodique a partir de ses valeurs nodales. Si(i=0,...,N). On donne une representation explicite pour les moments S i (1) (i=0,...N)

Développements asymptotiques de fonctions splines avec partage uniforme de la droite réelle

This paper considers the determination of interpolating spline functions over a uniform mesh of the real line when the nodes are uniformly shifted. Asymptotic expansions are obtained from linear dependence relationships and convergence results are established using Peano kernels. Then a posteriors improvements for interpolating splines are deduced. The results are extended to cover histospline functions.

ON CIRCULANT MATRICES FOR CERTAIN PERIODIC SPLINE AND HISTOSPLINE PROJECTIONS

and its k derivativ (see [7]) . eThe regularity propertie os f the matrices p (v,P) are useful inestablishing existence results and, together with bounds for the uniformmatrix norm of the inverses, in obtaining convergence results (see [5]).The object of this paper is to review the properties of thepolynomials P

On consistency relations for polynomial splines on a uniform partition

In this paper we present linear dependence relations connecting spline values, derivative values and integral values of the spline. These relations are useful when spline interpolants or histospline projections of a function are considered.

Histospline projections on a uniform partition

Abstract We present a unified treatment of the periodic histospline projection of a function f on a uniform partition. We consider a given real number v ϵ [0, 1] and obtain existence and uniqueness results for the n -degree periodic spline s determined by the values { ∫ x i +vh x i +(v+1)h s(x)dx=0 N−1 . For a function f ∈ C p n + 1 [ a , b ] and a spline determined by the conditions ∫ x i +vh x i +(v+1)h s(x)dx= ∫ x i +vh x i +(v+1)h f(x)dx(i=0,…,N−1) we obtain error bounds of the form ‖ f ( k ) − s ( k ) ‖ ∞ ≃ O ( h n + 1 − k ) ( k = 0, …, n ).