Results 191 to 200 of about 3,479 (214)

A new computational GMRES method

Applied Mathematics and Computation, 2008
In this article, we present a new algorithm for the popular iterative method GMRES. In this method the weighted Arnoldi process is used and there is no need to Given rotations. The implementation of the algorithm has been tested by numerical examples. The numerical results show the method converges fast and works with high accuracy.
Hashem Saberi Najafi, H. Zareamoghaddam
openaire   +1 more source

A Note on the Superlinear Convergence of GMRES

SIAM Journal on Numerical Analysis, 1997
In this short paper it is shown how the rate of convergence of the generalized minimal residual (GMRES) method for solving a linear operator equation \((\lambda I + K) u = f\) in a Hilbert space is related to the degree of compactness of \(K\) measured by the products of its singular value.
openaire   +3 more sources

Implicitly restarted and deflated GMRES

Numerical Algorithms, 1999
We introduce a deflation method that takes advantage of the IRA method, by extracting a GMRES solution from the Krylov basis computed within the Arnoldi process of the IRA method itself. The deflation is well-suited because it is done with eigenvectors associated to the eigenvalues that are closest to zero, which are approximated by IRA very quickly ...
C. Le Calvez, Brígida Molina
openaire   +2 more sources

Complementary cycles of restarted GMRES

Numerical Linear Algebra with Applications, 2008
AbstractRestarted GMRES is one of the most popular methods for solving large nonsymmetric linear systems. It is generally thought that the information of previous GMRES cycles is lost at the time of a restart; therefore, each cycle contributes to the global convergence individually. However, this is not the full story.
Baojiang Zhong, Ronald B. Morgan
openaire   +2 more sources

Parallelism in ILU-preconditioned GMRES

Parallel Computing, 1998
Abstract A parallel implementation of the preconditioned GMRES method is described. The method is used to solve the discretized incompressible Navier–Stokes equations. A parallel implementation of the inner product is given, which appears to be scalable on a massively parallel computer. The most difficult part to parallelize is the ILU-preconditioner.
Cornelis Vuik, R. R. P. van Nooyen, P. Wesseling   +2 more
openaire   +1 more source

A new variant of restarted GMRES

Numerical Linear Algebra with Applications, 1999
The topic of this paper is a new variant of restarted generalized minimal residual (GMRES) method for solving large linear systems. The author gives an alternative form of minimal residual condition based on the construction of a polynomial which is smaller than GMRES residual one near the origin and this is used in the case of slow convergence of the ...
openaire   +2 more sources

On the role of orthogonality in the GMRES method

1996
In the paper we deal with some computational aspects of the Generalized minimal residual method (GMRES) for solving systems of linear algebraic equations. The key question of the paper is the importance of the orthogonality of computed vectors and its influence on the rate of convergence, numerical stability and accuracy of different implementations of
Miroslav Rozlozník, Zdenek Strakos, Miroslav Tuma   +2 more
openaire   +1 more source

Expressions and Bounds for the GMRES Residual

BIT Numerical Mathematics, 2000
The author discusses the generalized minimal residual method (GMRES) for the iterative solution of a linear system and derives expressions and bounds for the residual norm in this algorithm. The minimal residual norm is expressed in terms of the pseudo-inverse of the next Krylov matrix. The minimal residual norm of a scaled Jordan block is expressed in
openaire   +1 more source

On the Residual Norm in FOM and GMRES

SIAM Journal on Matrix Analysis and Applications, 2011
We provide expressions for the residual norms when using the full orthogonalization method and the generalized minimum residual method for solving linear systems. They involve a triangular submatrix of the Hessenberg matrix generated by the Arnoldi process.
openaire   +1 more source

A Generalized GMRES Iterative Method

2001
We describe a generalization of the GMRES iterative method in which the residual vector is no longer minimized in the 2-norm but in a C-norm, where C is a symmetric positive definite matrix. The resulting iterative method call GGMRES is derived in detail and the minimizing property is proven.
David R. Kincaid, Jen-Yuan Chen, David M. Young   +2 more
openaire   +1 more source