非线性方程根的一种估计方法  

A method of estimation of nonlinear equation roots

作　　者：彭博[1] 唐烁[1] PENG Bo;TANG Shuo(School of Mathematics,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学数学学院,合肥230009

出　　处：《应用数学与计算数学学报》2018年第4期959-968,共10页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(61272024)

摘　　要：一些非线性方程的根难以求解,但在满足一定精度的前提下,考虑求解其根的范围问题是可行的.利用数论中经典的序贯搜索(SNTO)将非线性方程和多项式方程联系起来,用友矩阵将多项式的根和矩阵的特征值关联起来,进而通过对矩阵特征值的探讨来估计非线性方程根的范围.数值实例验证了该算法的有效性.It is difficult to solve the roots of some nonlinear equations.While under the premise of promising precision,it is feasible to solve the scope of the roots.In this paper,the nonlinear equation and the polynomial equation are connected by the sequential number theoretic optimization method,and the roots of the polynomial equation and the matrix eigenvalues are linked by the friend matrix.Therefore,the scope of the roots of the nonlinear equation could be estimated.The numerical example verifies the effectiveness of the algorithm.

关 键 词：数论网格 友矩阵 特征值 圆盘定理 

分 类 号：O151.1[理学—数学]