在寻找根源的过程中采用回火方法
Junghyo Jo1,2,3, Alexandre Wagemakers4, Vipul Periwal5
1Department of Physics Education, <a href="https://ror.org/04h9pn542">Seoul National University</a>, Seoul 08826, Korea.
Physical review. E
|September 19, 2024
概括
这项研究引入了一种新的参数化的牛顿-拉普森方法,用于更快,更强大的根查找. 它受到物理学的启发,为数值方法提供了一个回火方法.
科学领域:
- 数字分析 数字分析
- 计算物理 计算物理
背景情况:
- 牛顿-拉普森方法是解决方程数值的基石.
- 它的应用涵盖了包括物理在内的各种科学学科.
- 加强其融合和稳健性仍然是一个活跃的研究领域.
研究的目的:
- 介绍牛顿-拉普森方法的新型参数化变体.
- 为了利用物理原理来改进数值根的寻找.
- 探索连接与系列扩展方法.
主要方法:
- 开发一个参数化的牛顿-拉普森算法.
- 对方法属性的分析验证.
- 经验测试趋同和稳定性.
- 建立与阿多米数列方法的联系.
主要成果:
- 参数化的方法显示了增强的稳定性.
- 在根查找代中观察到更快的融合率.
- 引入的参数使得一种新的回火方法成为可能.
- 与阿多米数列的连接在数学上得到了建立.
结论:
- 参数化的牛顿-拉普森方法比标准技术提供了显著的改进.
- 这种以物理为灵感的参数为数值优化提供了一个新的维度.
- 这项工作为先进的代根查找算法开辟了道路.
相关概念视频
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
45
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
45
02:27Basic Plant Anatomy: Roots, Stems, and Leaves
58.7K
The primary organs of vascular plants are roots, stems, and leaves, but these structures can be highly variable, adapted for the specific needs and environment of different plant species.
58.7K