On a Non-stagnation Condition for Gmres and Application to Saddle Point Matrices
نویسنده
چکیده
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. The analysis is then explored in the context of saddle point matrices, when these are preconditioned in a way so as to lead to nonsymmetric and indefinite systems. Our results indicate that these matrices may represent an insightful training set towards the understanding of the interaction between indefiniteness and stagnation.
منابع مشابه
Generalized iterative methods for solving double saddle point problem
In this paper, we develop some stationary iterative schemes in block forms for solving double saddle point problem. To this end, we first generalize the Jacobi iterative method and study its convergence under certain condition. Moreover, using a relaxation parameter, the weighted version of the Jacobi method together with its convergence analysis are considered. Furthermore, we extend a method...
متن کاملOptimization of the parameterized Uzawa preconditioners for saddle point matrices
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 ...
متن کاملPreconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation
Introduction Fractional differential equations (FDEs) have attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme may be a good approach, particularly, the schemes in numerical linear algebra for solving ...
متن کاملUnsteady Heat and Mass Transfer Near the Stagnation-point on a Vertical Permeable Surface: a Comprehensive Report of Dual Solutions
In this paper, the problem of unsteady mixed convection boundary layer flow of a viscous incompressible fluid near the stagnation-point on a vertical permeable plate with both cases of prescribed wall temperature and prescribed wall heat flux is investigated numerically. Here, both assisting and opposing buoyancy forces are considered and studied. The non-linear coupled partial differential equ...
متن کاملNew conditions for non-stagnation of minimal residual methods
In the solution of large linear systems, a condition guaranteeing that a minimal residual Krylov subspace method makes some progress, i.e., that it does not stagnate, is that the symmetric part of the coefficient matrix be positive definite. This condition results in a well-established worst-case bound for the convergence rate of the iterative method, due to Elman. This bound has been extensive...
متن کامل