CAJ | 학술논문

Essai对求解非对称线性方程组的广义极小残差法(GMRES)进行改进，提出加权GMRES方法(WGMRES)。该方法具有良好的收敛效果，但计算量较大。本文利用加权GMRES本身构造出一种有效的多项式预处理并与加权GMRES结合，构造了一种新算法。该算法能够显著地减少加权GMRES迭代次数，并能减少运算量和储存量。数值算例表明，相对于加权GMRES方法来说，新算法减少了运算时间和迭代次数。
Essai대구해비대칭선성방정조적엄의겁소잔차법(GMRES)진행개진，제출가권GMRES방법(WGMRES)。해방법구유량호적수렴효과，단계산량교대。본문이용가권GMRES본신구조출일충유효적다항식예처리병여가권GMRES결합，구조료일충신산법。해산법능구현저지감소가권GMRES질대차수，병능감소운산량화저존량。수치산례표명，상대우가권GMRES방법래설，신산법감소료운산시간화질대차수。
Essai presented a weighted GMRES method (GMRES) by improving GMRES method to solve nonsymmetric linear systems. The method has good convergence, but the computation cost is increasing. In this paper, we propose an efficient polynomial precondi-tioner based on WGMRES, and obtain a new algorithm. Numerical experiments indicate that the new algorithm can considerably reduce the iterative steps and computation cost.