Performance comparison of preconditioned iterative methods with direct preconditioners
Consider the matrix \(A=I-L-U\), a decomposition of the matrix \(A\) into a diagonal, a lower- and an upper triangular part. To solve \(Ax=b\), the preconditioners \(P\) of the form \(P_l=I+\beta L\), \(P_u=I+\beta U\), or \(P_b=I+\beta(L+U)\) can be applied. Then the original and the preconditioned system can be solved by an AOR (accelerated overrelaxation) iterative method. Comparison theorems are given for the (spectral radius of the) iteration matrices of the AOR methods with and without preconditioning. A near optimal selection of the parameter \(\beta\) for the Krylov method is proposed for each of the preconditioners.
scientific article; zbMATH DE number 6362185