On the Number and Locations of the Eigenvalues of Generalized Eigenvalue Problem

The gerleralized eigenvalue problem Aχ=λBχ (1) where A and B are teal symmetric n×n matrices,is one 0f the basie Problems in matrix theory,which apPears in many fields,Such as physics,mechanics and engineering.When B is a positiVe definite matrix(1)can be solved by reducing it to the form     

换元Newton型方法的计算效能和最佳换元周期

考虑非线性方程组: F(x)=0, (1.1)其中F:R~n→R~n是二次连续可微函数.一般地说,解方程组(1.1)的拟Newton法较Newton法更为有效.我们可以将拟Newton法解释为逐次在R~n的子空间上构造F′(x)的近似(割线近似)得到的算法.按照这种思想,如果将子空间依次循环取成F′(x)的例