Abstract
Approximation theory experienced a long term history. Since 50’ last century, the rise of spline function as well as the advance of calculation promotes the growth of classical approximation theory and makes them develop a profound theory in maths, and application values have shown among the field of scientific calculation and engineering technology and etc. At present, the study of spline function had made a great progress and had a lot of fruits, as for that, the reader could look up the book [1] or [2]. Nevertheless, the research staff pays less attention to exponential spline function, since polynomial spline function is a special case of that, so it is much essential and meaningful for one to explore the nature of exponential spline function.
Highlights
We introduce the definition of exponential spline function
From literature [3], we could learn the definition: if function S (t ) satisfies equation L= S (t ) ∑ ckδ (t − tk ), we describe it as exponential k spline function, (0 ≤ i ≤ n) are where L is a differential operator Lf (=t )
= S ( xi ) f= ( xi ) i 0,1, N +1 = S′(a) f= ′(a) S′(b) f ′(b) there exist the 3rd degree exponential spline function satisfied with condition
Summary
We introduce the definition of exponential spline function. From literature [3], we could learn the definition: if function S (t ) satisfies equation L= S (t ) ∑ ckδ (t − tk ) , we describe it as exponential k spline function,(0 ≤ i ≤ n) are where L is a differential operator Lf (=t )constant coefficient and Dk representDn+1 f + an Dn f + + a0 D0 f kth-order derivative. We introduce the definition of exponential spline function. From literature [3], we could learn the definition: if function S (t ) satisfies equation L= S (t ) ∑ ckδ (t − tk ) , we describe it as exponential k spline function, (0 ≤ i ≤ n) are where L is a differential operator Lf (=t )
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