A Significant Improvement on Newton’s Iterative Method

Wu Xinyuan

Volume 20 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(8): 863-866

Wu Xinyuan. A Significant Improvement on Newton’s Iterative Method[J]. Applied Mathematics and Mechanics, 1999, 20(8): 863-866.

Citation:

Wu Xinyuan. A Significant Improvement on Newton’s Iterative Method[J]. Applied Mathematics and Mechanics, 1999, 20(8): 863-866.

Citation:

Wu Xinyuan. A Significant Improvement on Newton’s Iterative Method[J]. Applied Mathematics and Mechanics, 1999, 20(8): 863-866.

PDF( 1489 KB)

A Significant Improvement on Newton’s Iterative Method

Wu Xinyuan

Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

Received Date: 1997-04-14
Rev Recd Date: 1999-01-05
Publish Date: 1999-08-15

Abstract

Abstract

For solving nonlinear and transcendental equation f(x)=0, a singnificant improvement on Newton s method is proposed in this paper. New Newton Like methods are founded on the basis of Liapunovs methods of dynamic system. These new methods preserve qudratic convergence and computation efficiency of Newtons method, but remove the monotoneity condition imposed on f(x):f(x)≠0.
- nonlinear equation,
- transcendental equation,
- dynamic system,
- iterative method,
- Newton method,
- numerical analysis

FullText(HTML)

References(4)

References

[1]	Hale J K.Ordinary Differential Equations[M].Huntington,New York:Robert E Krieger Publishing Company,1982.
[2]	Hirsch M W,Smale S.Differential Equations,Dynamic Systems and Linear Algebra[M].New York and London:Academic Press,1974,192~193.
[3]	吴新元.解Stiff常微分方程的精确指数拟合法[J].南京大学学报(自然科学版),1997,31(1):1~6.
[4]	Traub J F.Solution of transcendental equations[A].In:A Ralston,H S Wilf Eds.Mathematical Methods for Digital Computers[C].Vol.New York:John Wiley & Sons,Inc,1968.

Relative Articles

[1]	WANG Jincheng, QI Jin, WU Chuijie. Analysis and Modelling of Optimal Dynamical Systems of Incompressible NavierStokes Equations[J]. Applied Mathematics and Mechanics, 2020, 41(1): 1-15. doi: 10.21656/1000-0887.400279
[2]	YANG Na, CHEN Longwei, XIONG Mei. Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302
[3]	WANG Ting, TANG Shuo. Construction of a Parametric Derivative-Free Iterative Method With Memory for Dynamic System Analysis[J]. Applied Mathematics and Mechanics, 2017, 38(12): 1342-1358. doi: 10.21656/1000-0887.370350
[4]	WANG Yi. Essential Consistency of Pressure Poisson Equation Method and Projection Method on Staggered Grid[J]. Applied Mathematics and Mechanics, 2011, 32(6): 741-745. doi: 10.3879/j.issn.1000-0887.2011.06.011
[5]	S. Abbasbandy, LIAO Shi-jun. A New Modification of False Position Method Based on the Homotopy Analysis Method[J]. Applied Mathematics and Mechanics, 2008, 29(2): 203-208.
[6]	LU Zai-hua, CHEN Zheng-han, FANG Xiang-wei, GUO Jian-feng, ZHOU Hai-qing. Structural Damage Model of Unsaturated Expansive Soil and Its Application in Multi-Field Couple Analysis on Expansive Soil Slope[J]. Applied Mathematics and Mechanics, 2006, 27(7): 781-788.
[7]	SHAO Xin-hui, SHEN Hai-long, LI Chang-jun. Stair Matrices and Their Generalizations With Applications to Iterative Methods[J]. Applied Mathematics and Mechanics, 2006, 27(8): 971-977.
[8]	LI Wen-cheng, DENG Zi-chen, HUANG Yong-an. Efficient Numerical Integrators for Highly Oscillatory Dynamic Systems Based on Modified Magnus Integrator Method[J]. Applied Mathematics and Mechanics, 2006, 27(10): 1211-1218.
[9]	YAO Yi-rong, ZHANG Lian-sheng, HAN Bo-shun. Newton Method for Solving a Class of Smooth Convex Programming[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1351-1358.
[10]	WANG Xi-cheng, GE Zeng-jie, WU Hong-yu. An Algebraic Multigrid Method for Coupled Thermo-Hydro-Mechanical Problems[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1307-1313.
[11]	HUANG Hu, ZHOU Xi-reng. On the Resonant Generation of Weakly Nonlinear Stokes Waves in Regions With Fast Varying Topography and Free Surface Current[J]. Applied Mathematics and Mechanics, 2001, 22(6): 651-660.
[12]	Nicolae Tarfulea. Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term[J]. Applied Mathematics and Mechanics, 2000, 21(3): 253-259.
[13]	TIAN Li-xin, CHU Zhi-jun, LIU Zeng-rong, JIANG Yong. Numerical Analysis of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1013-1020.
[14]	Yin Bangxin. Iterative Method on Large Deflection Nonlinear Problem of Laminated Composite Shallow Shells and Plates[J]. Applied Mathematics and Mechanics, 1999, 20(7): 721-728.
[15]	Chang Haiping, Huang Taiping. The Auto-Adjustable Damping Method for Solving Nonlinear Equations[J]. Applied Mathematics and Mechanics, 1998, 19(2): 151-155.
[16]	Tian Lixin, Xu Zhenyuan. The Research of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation[J]. Applied Mathematics and Mechanics, 1997, 18(10): 953-958.
[17]	Wang Shouxin, Liu Xiping, Peng Tianguo, Zhao Zhongsheng, Zhao Suhua. The BEM for Solving the Nonhomogeneous Helmholtz Equation with Variable Coefficients[J]. Applied Mathematics and Mechanics, 1996, 17(1): 81-85.
[18]	Chen Songlin. Singular Perturbation for a Class of Coupled Chemical Reaction and Diffusion Systems[J]. Applied Mathematics and Mechanics, 1995, 16(6): 511-517.
[19]	Li Jia-chun. Turbulent Coherent Structure and Dynamic System[J]. Applied Mathematics and Mechanics, 1991, 12(2): 171-176.
[20]	Liu Wei-jian, Jiang Wei-xing, Qu Zhi-hao. The Threo-Dimensional Analysis of the Self-Vib rational Characteristics of the 2050mm Hot-Strip Mill Housing by Means of Laser Holographic Interferometry and Finite Element Method[J]. Applied Mathematics and Mechanics, 1991, 12(3): 269-277.