论文标题
终点条件对分形插值功能的表示和整合的影响以及相关操作员的良好确定性
Impact of End Point Conditions on the Representation and Integration of Fractal Interpolation Functions and Well Definiteness of the Related Operator
论文作者
论文摘要
分形插值技术是经典插值方法的替代方法，尤其是在涉及混乱信号的情况下。用于构建分形插值功能的迭代功能系统的逻辑是将整个插值域分为子域，并分别对每个子域上定义功能。本文的目的是探讨终点条件对所得函数的图形表示及其数值集成的重要性。提出IFS的核心问题，即分形插值功能的连续性，以解释解决该问题的技术。分形插值函数代替分析表达，始终以递归关系表示。本文进一步提出了这些递归关系的推导，并提出了一种直接的方法，以找到与这些关系有关的近似函数。
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal interpolation functions is to divide the entire interpolating domain into subdomains and define functions on each subdomain piecewisely. The objective of this paper is to explore the significance of the end point conditions on the graphical representation of the resultant functions and their numerical integration. The central problem in the formulation of the IFS, the continuity of the fractal interpolation functions, is addressed with an explanation on the techniques implemented to resolve the problem. Instead of an analytical expression, the fractal interpolation functions are always represented in terms of recursive relations. This paper further presents the derivation of these recursive relations and proposes a straightforward method to find the approximating function, involved in these relations.
