Results 151 to 160 of about 733 (176)
Some of the next articles are maybe not open access.
Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing, 2010In many situations, it has been observed that significant convergence improvements can be achieved in preconditioned Krylov subspace methods by enriching them with some spectral information. On the other hand, effective preconditioning strategies are often designed where the preconditioner varies from one step to the next so that a flexible Krylov ...
Giraud, Luc +3 more
openaire +2 more sources
A new computational GMRES method
Applied Mathematics and Computation, 2008In 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.
H Saberi Najafi
exaly +2 more sources
Some observations on weighted GMRES [PDF]
Numerical Algorithms, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Güttel +2 more
exaly +6 more sources
Simpler GMRES with deflated restarting
Mathematics and Computers in Simulation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yiqin Lin, Liang Bao, Qinghua Wu
openaire +2 more sources
On GMRES-Equivalent Bounded Operators
SIAM Journal on Matrix Analysis and Applications, 2000The author studies the generalized minimal residual (GMRES) method applied to some operator equation \(Ax= r\) in a Hilbert space \(H\), where the operator \(A\in L(H)\) is supposed to be linear and bounded. At the \(k\)th step, the GMRES produces an approximate solution which minimizes the residual norm \(\|Ax-r\|\) over the Krylov subspace \(K^k(A,r):
openaire +2 more sources
Implicitly restarted and deflated GMRES
Numerical Algorithms, 1999We 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, 2008AbstractRestarted 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
A Note on the Superlinear Convergence of GMRES
SIAM Journal on Numerical Analysis, 1997In 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
Parallelism in ILU-preconditioned GMRES
Parallel Computing, 1998Abstract 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 +2 more
openaire +1 more source
On the role of orthogonality in the GMRES method
1996In 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 +2 more
openaire +1 more source