Results 71 to 80 of about 4,826 (176)

Notes on GMRES Algorithm Organization

, 2005
The Generalized Minimum Residual (GMRES) iterative method and variations of it are frequently used for solving systems of linear equations of the form Ax = b, where A is a large sparse nonsingular nonsymmetric matrix.
Richard J. Hanson, David R. Kincaid
core  

Efficient Numerical Schemes for a Heterogeneous Reaction–Diffusion System with Applications

Mathematics
In this study, a class of nonlinear heterogeneous reaction–diffusion system (RDS) has been considered that arises in modeling epidemiological interactions, environmental sciences, and chemical and ecological systems.
Samima Akhter, Md. Ariful Islam Arif, Rubayyi T. Alqahtani, Samir Kumar Bhowmik   +3 more
doaj   +1 more source

Computable convergence bounds for GMRES

, 1998
The main purpose of this paper is the derivation of computable bounds on the residual norms of (full) GMRES. The new bounds depend on the initial guess and thus are conceptually different from standard 'worst-case' bounds. The analysis is valid
Jörg Liesen
core  

Smoothing-norm preconditioning for GMRES [PDF]

, 2004
When GMRES is applied to a discrete ill-posed problem with a square matrix, then the iterates can be considered as regularized solutions. We show how to precondition GMRES in such a way that the iterations take into account a smoothing norm for the ...
Jensen, Toke Koldborg, Hansen, Per Christian   +1 more
core  

The performances of R GPU implementations of the GMRES method [PDF]

Revista Română de Statistică, 2018
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small fraction of ...
Bogdan Oancea, Richard Pospisil
doaj  

The Tortoise and the Hare restart GMRES [PDF]

, 2001
When solving large nonsymmetric systems of linear equations with the restarted GMRES algorithm, one is inclined to select a relatively large restart parameter in the hope of mimicking the full GMRES process.
Embree, Mark
core  

GMRES on (Nearly) Singular Systems

, 1994
. We consider the behavior of the gmres method for solving a linear system Ax = b when A is singular or nearly so, i.e., ill-conditioned. The (near) singularity of A may or may not affect the performance of gmres, depending on the nature of the system ...
Peter Brown, Peter N. Browny, Homer Walker, F. Walkerz, Homer   +4 more
core  

Extending Elman's bound for GMRES

Linear Algebra and its Applications
If the numerical range of a matrix is contained in the right half of the complex plane, the GMRES algorithm for solving linear systems will reduce the norm of the residual at every iteration. In his Ph.D. dissertation, Howard Elman derived a bound that guarantees convergence. When the numerical range contains the origin, GMRES need not make progress at
openaire   +2 more sources

POLYNOMIAL PRECONDITIONED GMRES AND GMRES-DR

, 2014
We look at solving large nonsymmetric systems of linear equations using polynomial preconditioned Krylov methods. We give a simple way to find the polynomial.
Quan Liu, Walter Wilcox, Ronald B. Morgan   +2 more
core  

An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method. [PDF]

Entropy (Basel), 2023
Chen JF, Gu XM, Li L, Zhou P.
europepmc   +1 more source