CAJ | 학술논문

针对大型稀疏鞍点问题给出了一种新的迭代解法,该方法的构成是基于对系数矩阵进行的一种分裂,A∈Rn×n是对称正定矩阵.利用不完全分解法分解A为LLT+R,通过适当选取预处理矩阵和待定系数,证明该迭代法是收敛的,并且以定理的形式给出了新迭代法收敛的充分必要条件.
침대대형희소안점문제급출료일충신적질대해법,해방법적구성시기우대계수구진진행적일충분렬,A∈Rn×n시대칭정정구진.이용불완전분해법분해A위LLT+R,통과괄당선취예처리구진화대정계수,증명해질대법시수렴적,병차이정리적형식급출료신질대법수렴적충분필요조건.
A new iterative solution is proposed to solve the problem of large-scale saddle point problem.Based on a splitting for the matrix of coefficients which A∈Rn×n is symmetric positive definite in coefficient matrix,using the incomplete decomposition method which split A to LLT+R,after choosing a pretreated matrix and undermined parameters,the converence of the iteration is proved and sufficient and necessary conditions of the new iteration method proposed becomes convergent in form of theorem.