CAJ | 학술논문

白中治等提出了解非埃尔米特正定线性方程组的埃尔米特和反埃尔米特分裂（HSS）迭代方法（BaiZZ，GolubGH，NgMK．Hermitian and skew-Hermitian splitting methods for non—Hermitian positive definite linearsystems．SIAM，Matrix Anal．Appl．，2003，24：603-626）．本文精确地估计了用HSS迭代方法求解广义鞍点问题时在加权2一范数和2一范数下的收缩因子．在实际的计算中，正是这些收缩因子而不是迭代矩阵的谱半径，本质上控制着HSS迭代方法的实际收敛速度．根据文中的分析，求解广义鞍点问题的HSS迭代方法的收缩因子在加权2．范数下等于1，在2一范数下它会大于等于1，而在某种适当选取的范数之下，它则会小于1．最后，用数值算例说明了理论结果的正确性．
백중치등제출료해비애이미특정정선성방정조적애이미특화반애이미특분렬（HSS）질대방법（BaiZZ，GolubGH，NgMK．Hermitian and skew-Hermitian splitting methods for non—Hermitian positive definite linearsystems．SIAM，Matrix Anal．Appl．，2003，24：603-626）．본문정학지고계료용HSS질대방법구해엄의안점문제시재가권2일범수화2일범수하적수축인자．재실제적계산중，정시저사수축인자이불시질대구진적보반경，본질상공제착HSS질대방법적실제수렴속도．근거문중적분석，구해엄의안점문제적HSS질대방법적수축인자재가권2．범수하등우1，재2일범수하타회대우등우1，이재모충괄당선취적범수지하，타칙회소우1．최후，용수치산례설명료이론결과적정학성．
The Hermitian and skew-Hermitian splitting （HSS） iteration method was presented and studied by Bai, et al. for solving non-Hermitian positive defi- nite linear systems （Bai Z Z, Golub G H, Ng M K. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J. Ma- trix Anal. Appl., 2003, 24：603 626）. In this paper, contraction factors of the HSS iteration method in terms of the weighted 2-norm and the 2-norm are given, respec- tively, for the generalized saddle point problems. These contraction factors rather than the spectral radius of the iteration matrix essentially control the actual conver- gent speed of the HSS iteration method in practical computations. According to the analyses, the contraction factor of the HSS iteration method for the generalized sad- dle point problem is one in the weighted 2-norm. However, it may be greater than or equal to one in the 2-norm and less than one in other suitable norms. Finally, numerical examples are used to examine the correctness of the theoretical results.