摘要
对于对称特征值问题,基于对原有复杂Jacobi共轭条件的简化,提出了一种修正的Jacobi共轭预处理梯度法.在理论上证明了在求解单个端部特征值时修正方法与原始方法有着渐近等价的共轭性.而在求解多个端部特征值时,修正方法与原始方法展现出极为相似的收敛性,但其矩阵乘积运算更少,因而计算代价也更小.数值算例进一步验证了修正方法的有效性和优越性.
For the symmetric eigenvalue problems, a modified Jacobi-conjugate preconditioned gradient method based on a simplification of the original complicated Jacobi-conjugation condition is proposed. Theoretical analysis shows that the modified method employs asymptotically equivalent conjugation to that of the original one for the single-vector iteration when one extreme eigenpair is computed. While for the block iteration to detect several extreme eigenpairs, the modified method exhibits remarkably similar convergence to that of the original one, but with much cheaper computational expenses due to less matrix multiplications. Numerical examples further demonstrate the effectiveness and superiority of the modified method.
出处
《应用数学与计算数学学报》
2013年第2期260-288,共29页
Communication on Applied Mathematics and Computation
