摘要
对于一般的非线性方程组的条件数,先根据矩阵范数的连续性给出了闭凸集上范数的有界性结论,再由范数的有界性和函数的G-可微性得出了其界的估计结果;对于方程组系数是方阵的情形,由范数有界性给出了一般性结论.
To obtain the condition number of the general nonlinear equations, a study was performed to draw a conclusion about the boundedness of norms in closed convex set according to the continuity of matrix norms. Then the estimated result of the bounds of condition numbers can be obtained based on the boundedness of norms and G-differentiability of functions. Moreover, some general conclusions about the boundedness of norms were given for the case that the coefficients of the equations form a square matrix.
出处
《河海大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第3期356-358,共3页
Journal of Hohai University(Natural Sciences)
关键词
非线性方程组
条件数
界的估计
nonlinear equations
condition number
estimation of bound
