求解Sylvester张量方程的隐式共轭梯度法

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 coefficient matrix is symmetric positive definite and the tensor on the right hand side is rank 1.The approximate 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.