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关于对称不定线性方程组Ax=b的一种求解算法
引用本文:陈文辉.关于对称不定线性方程组Ax=b的一种求解算法[J].新疆大学学报(理工版),1989,6(1):45-54.
作者姓名:陈文辉
作者单位:新疆大学数学系
摘    要:本文针对系数矩阵A具有少数几个正(负)特征值的对称不定性方程组Ax=b构造了一个有效的稳定算法.这个算法充分利用了矩阵的对称性及具有少数几个正(或负)特征值的特点,其运算量与Cholesky方法相当,大约为?个乘法和加法,所用贮存单元为?.从第四节的数值例子可以看出在上述假定条件下用本算法求解较Parlett和Reid算法要好些.尤其对A又是大型稀疏矩阵更为有效.

关 键 词:稳定算法  对称性  特征值  Newton位移  有理的QR变换

An Algorithm For Solving Symmetric Indefinite Systems of Linear Equations
Chen Wenhui.An Algorithm For Solving Symmetric Indefinite Systems of Linear Equations[J].Journal of Xinjiang University(Science & Engineering),1989,6(1):45-54.
Authors:Chen Wenhui
Institution:Chen Wenhui
Abstract:In this paper,we describle a fast,stable algorithm for solving symmetric inde-finite systems of linear equations Ax=b,the main idea of which is to take full advantage of the symmetry and few positive (or negative) eigenvalues of A.The number of operations involved in the algorithm are n~3/6 O(n~2) multiplications and additions,and n~2/2 O(n) storages are needed.From the examples given in 4,this algorithm is better than the algorithm provided by Parlett and Reid in above hypothsis,it is more effective that A is a Iarge matrix.
Keywords:stable algorithm  symmetry  eigenvalues  Newton shift  retional QR transformation
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