大型稀疏矩阵的不完全因子分解法及预处理

AN INCOMPLETE FACTORIZATION TECHNIQUE AND PRECONDITION METHODS FOR THE LARGE SPARSE MATRIX

本文对大型稀疏矩阵线性方程组的不完全因子分解及预处理法进行了研究．对对称正定阵和Ｌ阵分别提出了非对角元乘子不完全因子分解法的分解公式．对分解Ａ＝Ｍ－Ｎ，得到了当Ａ为对称正定时，Ｍ亦为对称正定；当Ａ为Ｌ阵时，分解为正规分裂等结果．并研究了预处理ＣＧ加速．

This paper describes an incomplete factorization technique called the non diagonal factors shifted incomplete factorization for positive definite matrix and L Matrix. The technique combines precondition methods for large sparse linear systems of which the coefficient matrix is positive definite matrix. The non diagonal factors shifted incomplete factorization produces a splitting of the matrix A is A=M-N, it is shown that if A is positive definite, then M is positive definite; if A is L Matrix, then the splitting A=M-N is regular splitting.