摘要
利用定积分几何意义,推导出经典牛顿法、算术平均牛顿法和调和平均牛顿法,结合Lagrange插值定义,提出了一类新的六阶收敛的平均值牛顿迭代法。该算法每次迭代只需要计算两个函数值和两个一阶导数值,有效避免对函数进行高阶求导。收敛性分析和数值实例进一步验证该算法在求解非线性方程迭代时比牛顿迭代法、算术平均牛顿法和调和平均牛顿法效率更高、速度更快。
Using the geometric meaning of definite integral, the classical Newton method, arithmetic mean Newton method and harmonic mean Newton method are deduced. Combined with the definition of Lagrange interpolation, a new mean Newton iteration method with sixth-order convergence is proposed. Each iteration of the algorithm only needs to calculate two function values and two first-order derivative values, which effectively avoids high-order derivatives of functions. Convergence analysis and numerical examples further verify that the algorithm is more efficient and faster than Newton iteration method, arithmetic mean Newton method and harmonic mean Newton method in solving nonlinear equations interactively.
作者
郭巧
杨兵
吴昌广
Guo Qiao;Yang Bing;Wu Changguang(Anhui Vocational and Technical College,Hefei 230611,China;Nanjing University of Science And Technology,Nanjing 210000,China)
出处
《廊坊师范学院学报（自然科学版）》
2023年第1期8-12,共5页
Journal of Langfang Normal University(Natural Science Edition)
基金
2018年安徽省教育厅重大项目“基于原子层沉积(ALD)制备下一代高性能叠层薄膜晶体管及界面调控机理的研究”(KJ2018ZD060)
2020年安徽教育厅高校优秀青年支持项目“基于静电纺丝法制备高性能薄膜晶体管及应用在逻辑电路”(gxyq2020108)
2020年度安徽省教育厅教学示范课“冲压成形工艺与模具设计”(2020SJJXSFK1415)
2020年度安徽职业技术学院校级科技工程项目“基于3D打印技术的智能舌诊仪结构优化及模具设计”(azy2020kj07)。
