求解非线性方程的多步区间迭代法
Multi-Step Interval Iteration Methods for Nonlinear Equation
DOI: 10.12677/AAM.2020.98132, PDF,  被引量    科研立项经费支持
作者: 楚 雪, 肖 旺, 王海军：中国矿业大学数学学院，江苏 徐州
关键词: 非线性方程；两步区间牛顿法；区间King迭代法；Nonlinear Equation； Two-Step Interval Newton Method； Interval King Operator
摘要: 本文首先介绍了非线性方程的相关知识，然后建立了求解非线性方程的两种高阶区间迭代法，并给出了相关的收敛性证明。最后通过数值算例验证新提出的区间迭代法的有效性。
Abstract: This paper first introduces the nonlinear equation and their related knowledge, then establishes two high order interval iterative methods for nonlinear equation and gives the relevant convergence proof. Finally, numerical examples are given to verify the effectiveness of the new interval iteration methods.
文章引用：楚雪, 肖旺, 王海军. 求解非线性方程的多步区间迭代法[J]. 应用数学进展, 2020, 9(8): 1124-1133. https://doi.org/10.12677/AAM.2020.98132

参考文献

[1] Tsai, L.W. and Morgan, A.P. (1985) Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods. Journal of Mechanical Design, 107, 189-200. [Google Scholar] [CrossRef] 
[2] 陈航. 三自由度并联机构正解及试验平台控制方法研究[D]: [硕士学位论文]. 武汉: 华中科技大学, 2005.
[3] Gau, C.Y. and Stadtherr, M.A. (2002) New Interval Methodologies for Reliable Chemical Process Modeling. Computers and Chemical Engineering, 26, 827-840. [Google Scholar] [CrossRef] 
[4] Meintjes, K. and Morgan, A.P. (1987) A Methodology for Solving Chemical Equilibrium Systems. Applied Mathematics and Computation, 22, 333-361. [Google Scholar] [CrossRef] 
[5] 杨圻, 陈展辉. 中国宏观外债适度规模研究[J]. 数量经济技术经济研究, 2001(11): 20.
[6] 胡志强, 陈健云, 陈万吉, 林皋, 李学文. 弹塑性接触问题的非光滑非线性方程组方法[J]. 计算力学学报, 2003, 20(6): 684-690.
[7] Wang, H.J. and Cao, D.X. (2009) Interval Expansion Method for Nonlinear Equation in Several Variables. Applied Mathematics and Computation, 212, 153-161. [Google Scholar] [CrossRef] 
[8] Ortega, J.M. and Rheinboldt, W.C. (1970) Iterative Solution of Nonlinear Equations in Several Variables. Volume 30, SIAM, Philadelphia.
[9] Moore, R.E. (1966) Interval Analysis. Volume 4, Prentice-Hall, Englewood Cliffs.
[10] 王德人, 张连生, 邓乃扬. 非线性方程的区间算法[M]. 上海: 上海科学技术出版社, 1987.
[11] Moore, R.E., Kearfott, R.B. and Cloud, M.J. (2009) Introduction to Interval Analysis. SIAM, Philadelphia. [Google Scholar] [CrossRef] 
[12] Bakhtiari, P., Lotfi, T., Mahdiani, K. and Soleymani, F. (2013) Interval Ostrowski-Type Methods with Guaranteed Convergence. Annalidell’Universita’di Ferrara, 59, 221-234. [Google Scholar] [CrossRef] 
[13] Amat, S., Busquier, S. and Plaza, S. (2004) Review of Some Iterative Root-Finding Methods from a Dynamical Point of View. Scientia, 10, 3-35.
[14] King, R.F. (1973) A Family of Fourth Order Methods for Nonlinear Equations. SIAM Journal on Numerical Analysis, 10, 876-879. [Google Scholar] [CrossRef] 
[15] Rump, S.M. (1999) INTLAB-Interval Laboratory. Springer, Berlin. [Google Scholar] [CrossRef] 

为你推荐