TY - GEN

T1 - On the relations between finite differences and derivatives of cardinal spline functions

AU - Morsche, ter, H.G.

PY - 1976

Y1 - 1976

N2 - Let m be a natural number and let Sm denote the class of cardinal spline functions of degree m. The object of this note is to establish a linear relationship between the 2m+2 quantities s(i+x), s(i+1+x),...,s(i+m+x), s(k)(i+y), s(k)(i+1+y),...,s(k)(i+m+y), where x,y ∈ [0,1], i=0,±1,±2,... s ∈ Sm and where s(k) denotes the k-th derivative of s (k=0,1,2,...,m−1). Using the shift operator E, we represent this relation in a simple form, involving the exponential Euler polynomials. The results are applied to cardinal spline interpolation.

AB - Let m be a natural number and let Sm denote the class of cardinal spline functions of degree m. The object of this note is to establish a linear relationship between the 2m+2 quantities s(i+x), s(i+1+x),...,s(i+m+x), s(k)(i+y), s(k)(i+1+y),...,s(k)(i+m+y), where x,y ∈ [0,1], i=0,±1,±2,... s ∈ Sm and where s(k) denotes the k-th derivative of s (k=0,1,2,...,m−1). Using the shift operator E, we represent this relation in a simple form, involving the exponential Euler polynomials. The results are applied to cardinal spline interpolation.

U2 - 10.1007/BFb0079749

DO - 10.1007/BFb0079749

M3 - Conference contribution

SN - 978-3-540-07543-1

T3 - Lecture Notes in Mathematics

SP - 210

EP - 219

BT - Spline Functions (Proceedings International Symposium, Karlsruhe, Germany, 1975)

A2 - Boehmer, K.

A2 - Meinardus, G.

A2 - Schempp, W.

PB - Springer

CY - Berlin

ER -