关键词: 特征值, 谱条件数, 预条件矩阵, 广义SOR算法, 预条件共轭梯度算法, Stokes方程

Abstract: The estimation for the bounds of the eigenvalues of matrix B^TA^-1B is studied on the assumption that the matrix A is symmetric and positive definite (SPD) and B has full column rank. Furthermore, the estimation for the spectral condition number of B^TA^-1B is obtained. Based on what was concluded above, it is proved that Q=B^TB is a good preconditioner for matrix B^TA ^-1B provided A is well conditioned. In the numerical experiment, the Stokes equation is solved by preconditioned conjugate gradient method (PCG). The experimental result demonstrates that Q=B^TB is indeed an effective preconditioner. This result is consistent to the numerical results of some references.