《计算机应用研究》|Application Research of Computers

一类不可微方程组的区间算法

Interval algorithm for one class of non-differentiable equations

免费全文下载 (已被下载 次)  
获取PDF全文
作者 刘风华
机构 1.中国矿业大学 信息与电气工程学院,江苏 徐州 221008;2.徐州工程学院 数学与物理科学学院,江苏 徐州 221008
统计 摘要被查看 次,已被下载
文章编号 1001-3695(2013)12-3540-03
DOI 10.3969/j.issn.1001-3695.2013.12.005
摘要 针对不可微方程组—绝对值方程Ax+B|x|=b的数值解问题进行研究, 提出了通过构造极大熵函数和新的区间算子对方程进行求解的区间极大熵算法。该算法能同时求出绝对值方程的近似解和估算其近似解的误差限, 并在A的奇异值全部大于|B|的奇异值时, 证明了算法的收敛性且收敛速度至少是线性的。理论分析和数值结果均表明提出的算法是有效的。
关键词 绝对值方程;极大熵;区间算子;区间算法
基金项目 国家自然科学基金资助项目(31270577)
徐州工程学院校科研基金资助项目(XKY2011101)
本文URL http://www.arocmag.com/article/01-2013-12-005.html
英文标题 Interval algorithm for one class of non-differentiable equations
作者英文名 LIU Feng-hua
机构英文名 1. School of Information & Electrical Engineering, China University of Mining & Technology, Xuzhou Jiangsu 221008, China; 2. School of Mathematics & Physical Science, Xuzhou Institute of Technology, Xuzhou Jiangsu 221008, China
英文摘要 This paper concerned with the non-differentiable equations and the absolute value equations. Based on maximum entropy and a new interval opeator, this paper proposed a interval maximum entropy algorithm which could solve the absolute value equations and estimate error between real solution and approximate solution. It proved the convergence and linear convergent rate when the singular values of A exceeded the singular value of |B|. Theoretic analysis and numerical results show the method is effective.
英文关键词 absolute value equations; maximum entropy; interval operator; interval algorithm
参考文献 查看稿件参考文献
  [1] ROHN J. Systems of interval linear equations[J] . Linear Algebra Applications, 1989, 126(12):39-78.
[2] ROHN J. A theorem of the alternatives for the equation Ax+B|x|=b[J] . Linear and Multilinear Algebra, 2004, 52(6):421-426.
[3] ROHN J. On unique solvability of the absolute value equation[J] . Optimization Letters, 2009, 3(4):603-606.
[4] MANGASARIAN O L, MEYER R R. Absolute value equations[J] . Linear Algebra and Applications, 2006, 419(2-3):359-367.
[5] MANGASARIAN O L. Absolute value programming[J] . Computational Optimization and Applications, 2007, 36(1):43-53.
[6] MANGASARIAN O L. Knapsack feasibility as an absolute value equation solvable by successive linear programming[J] . Optimization Letters, 2009, 3(2):161-170.
[7] NEMIROVSKII A. Several NP-hard problems arising in robust stability analysis[J] . Mathematics of Control, Signals, and System, 1999, 6(2):99-105.
[8] MANGASARIAN O L. A generalized Newton method for absolute value equations[J] . Optimization Letters, 2009, 3(1):101-108.
[9] ZHANG C, WEI Q J. Global and finite convergence of a generalized Newton method for absolute value equations[J] . Optimization Theory and Applications, 2009, 143(2):391-403.
[10] CACCETTA L, QU Biao, ZHOU Guang-lu. A globally quadratically convergent method for absolute value equations[J] . Computational Optimization and Applications, 2011, 48(1):45-58.
[11] WANG Hai-jun, LIU Hao, CAO Su-yu. A verification method for enclosing solutions of absolute value equations[J] . Collectanea Mathematica, 2013, 64(1):17-38.
收稿日期
修回日期
页码 3540-3542
中图分类号 TP301.6
文献标志码 A