Some applications for Newton - Krylov methods with a safeguard for GMRES ( m ) ∗
نویسندگان
چکیده
Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES(m), GMRESH(m) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate the efficiency of the proposed strategy.
منابع مشابه
Tensor-Krylov Methods for Solving Large-Scale Systems of Nonlinear Equations
This paper develops and investigates iterative tensor methods for solving large-scale systems of nonlinear equations. Direct tensor methods for nonlinear equations have performed especially well on small, dense problems where the Jacobian matrix at the solution is singular or ill-conditioned, which may occur when approaching turning points, for example. This research extends direct tensor metho...
متن کاملOn the similarities between the quasi-Newton least squares method and GMRes
We show how the quasi-Newton least squares method (QN-LS) relates to Krylov subspace methods in general and to GMRes in particular.
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 کاملTheoretical results on the global GMRES method for solving generalized Sylvester matrix equations
The global generalized minimum residual (Gl-GMRES) method is examined for solving the generalized Sylvester matrix equation [sumlimits_{i = 1}^q {A_i } XB_i = C.] Some new theoretical results are elaborated for the proposed method by employing the Schur complement. These results can be exploited to establish new convergence properties of the Gl-GMRES method for solving genera...
متن کاملKrylov Methods for Compressible Flows
In this paper we investigate the application of Krylov methods to compressible ows, and the e ect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, Approximate Factorization (AF) for structured grids, and ILU/GMRES for general grids are considered. Also, considered here, is Newton-Krylov matrix-free methods that we combine ...
متن کامل