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 -