福建师大福清分校学报
福建師大福清分校學報
복건사대복청분교학보
JOURNAL OF FUQING BRANCH OF FUJIAN NORMAL UNIVERSITY
2012年
2期
9-13
,共5页
Sherman-Morrison%正定%迭代法：矩阵分解
Sherman-Morrison%正定%迭代法：矩陣分解
Sherman-Morrison%정정%질대법：구진분해
Sherman-Morrison%positive definite matrix%iterative method%matrix decomposition
运用行列式、分块矩阵运算、正定矩阵的性质与Sherman-Morrison公式证明了正定矩阵的相关结论,结合正定矩阵性质得到了正定线性方程组的一种新的迭代解法和分解,相关的数值实验表明其算法计算量小,至多步比最速下降法快,比共轭梯度法效率高.
運用行列式、分塊矩陣運算、正定矩陣的性質與Sherman-Morrison公式證明瞭正定矩陣的相關結論,結閤正定矩陣性質得到瞭正定線性方程組的一種新的迭代解法和分解,相關的數值實驗錶明其算法計算量小,至多步比最速下降法快,比共軛梯度法效率高.
운용행렬식、분괴구진운산、정정구진적성질여Sherman-Morrison공식증명료정정구진적상관결론,결합정정구진성질득도료정정선성방정조적일충신적질대해법화분해,상관적수치실험표명기산법계산량소,지다보비최속하강법쾌,비공액제도법효솔고.
By application of determinant,block matrix,positive definite matrices and formula of Sherman-Morrison theorem,positive definite matrix correlation theorem can be obtained.And by combination of positive definite matrix properties,we can get a new method for positive definite linear equations iterative.The numerical experiments show that the algorithm has a small calculation amount and the most n step is faster than the steepest descent method and conjugate gradient method.
