求解非奇异线性方程组的正交降阶法

Orthogonal Reduced-Order Method for Solving Nonsingular Llinear Systems

基于Gram-Schmidt正交化方法提出了一种新的解线性方程组降阶的方法,证明了新的降阶方法是可行的,而且比Gram-Schmidt正交化QR方法解线性方程组运算量小,同时较QR方法以及LU分解方法解线性方程组数值更加稳定.最后,通过数值例子验证了新的降阶方法的有效性.

Based on the Gram-Schmidt QR method,a new orthonormal method for solving general linear systems was developed.The feasibility of the new method was proved,meanwhile it was demonstrated that the new method involves less arithmetic than the Gram-Schmidt QR method and have better numerical stability than the Gaussian elemenation and Gram-Schmidt QR method.The numerical examples show the effectiveness of the new method.