CAJ | 학술논문

对于大型线性代数方程组AX=b,通常采用单松弛因子进行超松弛迭代.作者在进行汽轮发电机氢内冷转子三维温度场的计算中,发现采用双松弛因子迭代比单松弛因子迭代速度更快.在深入研究的基础上,本文证明了在某种条件下,当A为时,双松弛因子迭代矩阵的谱半径小于单松弛因子迭代矩阵的谱半径.算例表明这种迭代格式的有效性.
대우대형선성대수방정조AX=b,통상채용단송이인자진행초송이질대.작자재진행기륜발전궤경내랭전자삼유온도장적계산중,발현채용쌍송이인자질대비단송이인자질대속도경쾌.재심입연구적기출상,본문증명료재모충조건하,당A위시,쌍송이인자질대구진적보반경소우단송이인자질대구진적보반경.산례표명저충질대격식적유효성.
For a large scale linear equations AX = b, if A has form as ,thispaper proves that using two relaxation factors would be better than conventional SOR iteration with single relaxation factor under some conditions. Some examples show the effectiveness of the scheme. The authors used two relaxation factors to calculate the 3D steady temperature distribution in a hydrogen inner-cooled turbogenerator rotor and got very good results.