带门槛不完全Cholesky分解存在的问题与改进

引言 许多物理应用问题求解的核心是如何高效求解稀疏线性方程组.直接解法由于在进行矩阵分解时常引入大量填充元,导致存储量与计算量一般很大,而且当系数矩阵条件数很大时,208数值计算与计算机应用2003年直接法稳定性差,使得任何中间舍入误差均可能引起最终计算结果

PROBLEMS AND IMPROVEMENTS TO THE INCOMPLETE CHOLESKY DECOMPOSITION WITH THRESHOLDS

In this paper, there have analyzed three problems occurred in the incomplete Cholesky factorization with thresholds for the matrices of symmetric positive definite. First, the drop strategy is used to only a row of the matrix at a time. Based on the idea of dropping the small elements in magnitude, this strategy is extended, that is, several rows of the factor are computed and the drop strategy is exploited for these rows at a time. Second, there may occur pivots of small magnitude or even negative ones. A solution is proposed in this paper. Finally, the incomplete factorization is often difficult to implement efficiently. Several integer vectors are exploited in this paper to solve this problem. Then the efficient implementation of the modified incomplete Cholesky decomposition is in consideration. Analyses and computation experiments show that these techniques are effective.