A variational approach to spline functions theory
A variational approach to spline functions theory
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样条函数理论的变分方法
DOI：
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发表时间：
2002
期刊：
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通讯作者：
G. Micula
中科院分区：
文献类型：
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作者：
G. Micula
样条函数已被证明在数值分析、微分方程、积分方程和偏微分方程的数值处理、统计学中非常有用，并在科学、工程、经济学、生物学、医学等领域得到了应用。众所周知，可以导出插值多项式样条作为某些变分问题的解。本文提出了样条插值的变分方法。通过考虑抽象Hilbert空间集合中相当一般的变分问题，我们导出了“抽象样条”的概念。本文的目的是提出一系列定理和结果，从Holladay关于自然三次样条的变分性质的经典结果开始，到抽象样条结果的一些一般变分方法。
Spline functions have proved to be very useful in numerical analysis, in numerical treatment of dierential, integral and partial differential equations, in statistics, and have found applications in science, engineering, economics, biology, medicine, etc. It is well known that interpolating polynomial splines can be derived as the solution of certain variational problems. This paper presents a variational approach to spline interpolation. By considering quite general variational problems in abstract Hilbert spaces setting, we derive the concept of ”abstract splines”. The aim of this paper is to present a sequence of theorems and results starting with Holladay’s classical results concerning the variational property of natural cubic splines and culminating in some general variational approach in abstract splines results.