In Simoncini and Szyld [Numer. Math., 109 (2008), pp. 477–487] a new non-stagnation condition for the convergence of GMRES on indefinite problems was proposed. In this paper we derive an enhanced strategy leading to a more general non-stagnation condition. Moreover, we show that the analysis also provides a good setting to derive asymptotic convergence rate estimates for indefinite problems. Th...

This contribution analyses residual generators that perfectly decouples disturbances in linear systems. The analysis focuses on the orders of the residual generators and it is shown how low order, local relationships in the model can be utilized to increase robustness properties. Easily computed bounds on minimum and maximum order residual generators are derived and presented. An upper bound on...

The parameterized Uzawa preconditioners for saddle point problems are studied in this paper. The eigenvalues of the preconditioned matrix are located in (0, 2) by choosing the suitable parameters. Furthermore, we give two strategies to optimize the rate of convergence by finding the suitable values of parameters. Numerical computations show that the parameterized Uzawa preconditioners can lead ...

In this paper we apply simple GMRES bounds to the nearly singular systems that arise in ill-posed problems. Our bounds depend on the eigenvalues of the coefficient matrix, the right-hand side vector and the nonnormality of the system. The bounds show that GMRES residuals initially decrease, as residual components associated with large eigenvalues are reduced, after which semi-convergence can be...

In this paper we compare two recently proposed methods, FGMRES 5] and GMRESR 7], for the iterative solution of sparse linear systems with an unsymmetric nonsingular matrix. Both methods compute minimal residual approximations using preconditioners, which may be diierent from step to step. The insights resulting from this comparison lead to better variants of both methods.

In this paper, we study the mean square convergence of the kernel least mean square (KLMS). The fundamental energy conservation relation has been established in feature space. Starting from the energy conservation relation, we carry out the mean square convergence analysis and obtain several important theoretical results, including an upper bound on step size that guarantees the mean square con...