在矩形域上对双变量分形插值函数的数值集成
1Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India.
The European physical journal. Special topics
|June 26, 2023
概括
这项研究引入了一种新的碎形数值整合方法,用于两变量信号. 这种方法为矩形数据集提供了精确的集成,并减少了对矩形数据集的计算力度.
科学领域:
- 数字分析 数字分析
- 碎形几何学 碎形几何学
- 科学计算科学计算
背景情况:
- 传统的数值集成方法可能是计算密集的.
- 碎形插值函数为函数近似提供了一种数据驱动的方法.
研究的目的:
- 为矩形区域的双变量数据推导一个碎形数值集成方法.
- 为了提高精度和减少数值集成中的计算力度.
- 分析拟议的碎形集成方法的收性质.
主要方法:
- 使用双变量分数插值函数的递归关系,构建分数的数值积分.
- 从数据点对代函数系统系数的评估.
- 基于这些系数的整合公式的推导.
- 与二线式插值函数的相关性.
- 导出垂直缩放因子公式以最大限度地减少近似误差.
主要成果:
- 提出了一种新的碎形数值积分公式.
- 该方法通过最小的计算来证明准确的结果.
- 建立了碎形方法与传统双重整合的融合.
- 对基准函数的数值分析验证了拟议的技术.
结论:
- 拟议的分形数值整合方法对于双变量数据有效.
- 该方法为传统技术提供了有效和准确的替代方案.
- 导出的垂直缩放因子有助于减少错误和趋同证明.
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