通过使用受约束最小平方的最小计算成本,为最小计算成本提供最优的零碎多项式近似
1Department of Electronic Engineering, Myongji University, Yongin 17058, Republic of Korea.
Sensors (Basel, Switzerland)
|June 27, 2024
概括
本研究介绍了一种最佳近似算法 (OPP),可以有效地将复杂的函数简化为片式多项式. 它尽量减少计算成本,同时保持准确性,这对于实时系统至关重要.
科学领域:
- 数字分析 数字分析
- 计算机科学 计算机科学
- 应用数学 应用数学 应用数学
背景情况:
- 简化非线性函数和离散数据对于计算效率至关重要.
- 现有的方法通常需要手动选择多项式顺序和间隔数,影响运行时间.
- 时间敏感的应用程序和嵌入式系统需要高精度和低计算成本的近似.
研究的目的:
- 提出一种最佳近似算法 (OPP) 用于将函数简化为片式多项式.
- 为了最大限度地降低计算成本,同时确保近似误差低于指定的值.
- 为了自动确定最佳多项式的顺序和间隔数.
主要方法:
- 使用受约束的最小平方来近似数据,用光滑的片式多项式.
- 开发一个算法,通过考虑计算成本和错误来搜索最佳的片式多项式 (OPP).
- 在目标CPU上对所有可能的多项式组合进行离线计算和计算成本的表格化.
- 采用随机选择方法来优化与给定的样本点的组合.
主要成果:
- OPP算法成功地确定了最佳的多项式顺序和间隔数.
- 通过选择符合误差容忍度的最低成本的OPP来最大限度地降低计算成本.
- 该算法在简化代表函数方面表现出有效的性能.
结论:
- 拟议的OPP算法为资源有限的环境中函数近似提供了一种有效的方法.
- 它自动选择最佳参数,减少手工劳动和提高性能.
- 这种方法对于准确性和运行时间效率都至关重要的应用非常有价值.
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