, On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems, J. Numer. Linear Algebra with Appl., 1 (1994), pp. 427--448.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....costly gmres process s times. It is also possible to make mhgmres more flexible, e.g. by varying m, or the number of times the Richardson phase is applied or monitoring the application of the polynomial on non seed residuals and stopping when the behavior is unsatisfactory. In light of results in [11, 12, 18] such flexibility is expected to enhance the performance of the algorithm; however, a full investigation remains to be done. 3.2. Error estimates for mhgmres. We seek bounds for the residual norms at each iteration of the method to restart, both before and after the application of the Richardson ....

....Eq. 3) will decrease after the Richardson phase. This is guaranteed irrespective of the value of m when A has definite symmetric part [3] Even then, however, kp(A)k might be very near 1 unless m is taken very large, thus making the method impractical. Then other methods might be preferable; see [12, 17, 27]. Theorem 3.2 and its corollary show how the approximation is governed by the effectiveness of the projections and the underlying gmres procedure, compounded by the application of the gmres polynomial. We also note that solving (2) for z j s is straighforward. An interesting but less stable ....

, On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems, J. Numer. Linear Algebra with Appl., 1 (1994), pp. 427--448.

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, On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems, J. Numer. Linear Algebra with Appl., 1 (1994), pp. 427--448.

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