计算机工程与科学
計算機工程與科學
계산궤공정여과학
COMPUTER ENGINEERING & SCIENCE
2009年
11期
156-158
,共3页
矩阵方程%极小范数解%最佳逼近%迭代算法
矩陣方程%極小範數解%最佳逼近%迭代算法
구진방정%겁소범수해%최가핍근%질대산법
the system of matrix equations%least-norm solution%optimal approximation solution%iterative method
矩阵方程组的求解在结构设计、参数识别、生物学、电学、分子光谱学、固体力学、自动控制理论、振动理论、有限元、线性最优控制等领域都有着重要应用.本文从解线性代数方程组的共轭梯度法中受到启示,不是采用传统的矩阵分解的方法,而是采用迭代算法给出了求矩阵方程组A_1XB_1＝C_1,A_2XB_2＝C_2的解、极小范数解及其最佳逼近解的方法.
矩陣方程組的求解在結構設計、參數識彆、生物學、電學、分子光譜學、固體力學、自動控製理論、振動理論、有限元、線性最優控製等領域都有著重要應用.本文從解線性代數方程組的共軛梯度法中受到啟示,不是採用傳統的矩陣分解的方法,而是採用迭代算法給齣瞭求矩陣方程組A_1XB_1＝C_1,A_2XB_2＝C_2的解、極小範數解及其最佳逼近解的方法.
구진방정조적구해재결구설계、삼수식별、생물학、전학、분자광보학、고체역학、자동공제이론、진동이론、유한원、선성최우공제등영역도유착중요응용.본문종해선성대수방정조적공액제도법중수도계시,불시채용전통적구진분해적방법,이시채용질대산법급출료구구진방정조A_1XB_1＝C_1,A_2XB_2＝C_2적해、겁소범수해급기최가핍근해적방법.
The problem of the system of matrix equations have been widely used in structural design, parametre identification, biology,electricity,molecular spectroscopy,solid mechanics,automatic control theory, vibration theory, finite elements, linear optimal control and so oa Many references have obtained a series important result by means of matrices decompositions, In this paper, we use an iterative method successfully in finding the solution of Matrix Equations A_1XB_1 =C_1 ,A_2XB_2 =C_2 and its least-norm solution op-timal approximation solution with the help of the method of convergence of conjugate.
