摘要
The restarted FOM method presented by Simoncini[7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method.
The restarted FOM method collinearity of all residuals is an efficient presented by Simoncini [7] according to the natural method for solving shifted systems, which generates the same Krylov subspace when the shifts are handled simultaneously. However, restarting slows down the convergence. We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach （restarted version） can converge more quickly than the restarted FOM method.
基金
Supported-by the National Natural Science Foundation of China(19971057)
the Science and Technology Developing Foundation of University in Shanghai of China(02AK41).
