A new way for LU-SGS approximate factorization deducing is proposed. 在LU近似因式分解的过程中,本文采用了一种新的推导方式。
The traditional methods are to solve the linear algebra equations directly, based on matrix factorization such as LU decomposition. 解线性代数方程组的传统方法是利用LU分解等直接求解,虽然传统方法具有理论上直接得到真解的优点,但当系数矩阵条件数很大时,存在严重的稳定性问题。
The investigation is based on three methods: the twisted factorization 、 LU factorization of tridiagonal matrix and expression the block inverse matrix with four block column vectors. And then three simple algorithms are derived. 分别基于块三对角矩阵的绞形分解、块LU分解和基于用四个分块的列向量表示块逆矩阵三种方法进行了研究,得到三个简单算法。