计算数学
計算數學
계산수학
MATHEMATICA NUMERICA SINICA
2010年
1期
47-58
,共12页
广义鞍点问题%ST分解%块三角预条件子%对称正定阵
廣義鞍點問題%ST分解%塊三角預條件子%對稱正定陣
엄의안점문제%ST분해%괴삼각예조건자%대칭정정진
generalized saddle point problem%ST decomposition%block triangular pre-conditioner%symmetric and positive definite matrix
本文对Golub和Yuan(2002)中给出的ST分解推广到广义鞍点问题上,给出了三种块预条件子,并重点分析了其中两种预条件子应用到广义鞍点问题上所得到的对称正定阵,得出了其一般的性质并重点研究了预处理矩阵条件数的上界,最后给出了数值算例.
本文對Golub和Yuan(2002)中給齣的ST分解推廣到廣義鞍點問題上,給齣瞭三種塊預條件子,併重點分析瞭其中兩種預條件子應用到廣義鞍點問題上所得到的對稱正定陣,得齣瞭其一般的性質併重點研究瞭預處理矩陣條件數的上界,最後給齣瞭數值算例.
본문대Golub화Yuan(2002)중급출적ST분해추엄도엄의안점문제상,급출료삼충괴예조건자,병중점분석료기중량충예조건자응용도엄의안점문제상소득도적대칭정정진,득출료기일반적성질병중점연구료예처리구진조건수적상계,최후급출료수치산례.
In this paper, we extend the ST decomposition which is given by Golub and Yuan (2002) to the generalized saddle point problem and present three block triangular preconditioners. Then we take two of them and apply them to the generalized saddle point problem. The two preconditioned systems are symmetric and positive definite. Then we deduce the general properties and the upper bound of the condition number of the two preconditioned systems one by one. Finally, numerical computation based on a particular linear system is given, which clearly shows the advantage.
