求解区间参数非线性方程组的数值方法
Numerical Method for Solving Nonlinear Equations with Interval Parameter

作者: 王琪 , 肖旺 , 王海军 :中国矿业大学数学学院,江苏 徐州;

关键词: 区间参数非线性方程组牛顿降阶法Krawczyk算子Nonlinear Equations with Interval Parameters Newton Order-Reduction Method Krawczyk Operator

摘要: 本文研究了区间参数非线性方程组的求解问题,通过改进区间Krawczyk算子并结合牛顿降阶法提出了求解区间参数非线性方程组的区间算法,给出了相关的理论结果和数值有效性测试。数值算例表明提出的算法可以有效的求解区间参数非线性方程组。

Abstract: In this paper, the problem of solving nonlinear equations with interval parameters is considered. By improving interval Krawczyk operator and applying Newton order-reduction method, we pro-pose an interval algorithm to solve nonlinear equations with interval parameters. The theoretical result and numerical test are given and numerical result shows that proposed interval algorithm can effectively solve nonlinear equations with interval parameters.

文章引用: 王琪 , 肖旺 , 王海军 (2017) 求解区间参数非线性方程组的数值方法。 应用数学进展, 6, 871-880. doi: 10.12677/AAM.2017.67105

参考文献

[1] Tsai, L.W. and Morgan, A.E. (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.
https://doi.org/10.1115/1.3258708

[2] Gau, C.Y. and Stadtherr, M.A. (2002) New Interval Methodologies for Reliable Chemical Process Modeling. Computers & Chemical Engineering, 26, 827-840.

[3] Meintjes, K. and Morgan, A.P. (1987) A Methodology for Solving Chemical Equilibrium Systems. Applied Mathematics and Computation, 22, 333-361.
https://doi.org/10.1016/0096-3003(87)90076-2

[4] Moore, R. (1966) Interval Analysis. Prentice-Hall, Inc., Englewood Cliffs, NJ.

[5] Krawczyk, R. (1969) Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken. [Newton-Algorithms for Evaluation of Roots with Error Bounds.] Computing, 4, 187-201.
https://doi.org/10.1007/BF02234767

[6] Hansen, E. (1992) Global Optimization Using Interval Analysis. Monographs and Textbooks in Pure and Applied Mathematics, Vol. 165, Marcel Dekker, NY.

[7] Nikas, I., Sotiropoulos, D. and Grapsa, T. (2006) Extending interval Newton Method for Nonlinear Parameterized Equations. In: Simos, T., Psihoyios, G. and Tsitouras, C., Eds., ICNAAM-International Conference on Numerical Analysis and Applied Mathematics, Wiley-VCH, Hersonisos, Crete, 512-515.

[8] Nikas, I. and Grapsa, T. (2009) Bounding the Zeros of an Interval Eq-uation. Applied Mathematics and Computation, 213, 466-478.
https://doi.org/10.1016/j.amc.2009.03.041

[9] 邱亮, 王海军, 王琪. 求解区间非线性方程的一类改进算法[J]. 应用数学进展, 2017, 6(5): 716-725.

[10] Moore, R.E. (1977) A Test for Existence of Solutions to Nonlinear Systems. SIAM Journal on Numerical Analysis, 14, 611-615.
https://doi.org/10.1137/0714040

[11] Alefeld, G. and Herzberger, J. (2012) Introduction to Interval Computation. Academic Press, Burlington.

[12] Zhang, D.Q., Li, W.G. and Shen, Z.H. (1999) Solving Underdetermined Systems with Interval Methods. Reliable Computing, 5, 23-33.
https://doi.org/10.1023/A:1026489507711

[13] 王德人, 张连生, 邓乃扬. 非线性方程组的区间算法[M]. 上海: 上海科学技术出版社, 1987: 30-31.

[14] Baumann, E. (1988) Optimal Centered Forms. BTL Numerical Mathematics, 28, 80-87.
https://doi.org/10.1007/BF01934696

[15] Wang, H.J. and Cao, D.X. (2009) Interval Expansion Method for Nonlinear Equation in Several Variables. Applied Mathematics and Computation, 212, 153-161.
https://doi.org/10.1016/j.amc.2009.02.008

[16] Moore, R.E. and Jones, S.T. (1977) Safe Starting Regions for Iterative Methods. SIAM Journal on Numerical Analysis, 14, 1051-1065.
https://doi.org/10.1137/0714072

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