求解Sylvester张量方程的隐式共轭梯度法  

Implicit conjugate gradient method for sylvester tensor equation

作　　者：陈震[1] 王炫盛[2] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵州贵阳550001 [2]中山大学深圳研究院,广东深圳518057

出　　处：《南昌大学学报（理科版）》2013年第2期127-130,共4页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11201092;11261012);贵州省科学技术基金资助项目(黔科合J字[20132207号)];贵州师范大学博士科研启动项目;江西省自然科学基金资助项目(2012ZBAB211001)

摘　　要：针对系数矩阵对称正定,右端张量秩1的Sylvester张量方程,提出隐式的共轭梯度法。这样得到的近似解、共轭方向和残量都具有张量的Tucker分解格式及递推关系。与标准的共轭梯度法求解Sylvester张量方程相比较,隐式共轭梯度法能够节约大量的计算量及存储空间。It present an implicit conjugate gradient method for the Sylvester tensor equation which the coef- ficient matrix is symmetric positive definite and the tensor on the right hand side is rank 1. The approxi- mate solution,the conjugate direction and the residual obtained by this method process not only the Tucker decomposition format but also simple iterative relation. Comparing with the standard conjugate gradient method for solving the Sylvester tensor equation, the algorithm proposed can reduce much computational cost and memory.

关 键 词：张量-矩阵乘法 Tucker分解 隐式共轭梯度法 

分 类 号：O241.6[理学—计算数学]