منابع مشابه
Weighted Inner Products for GMRES and GMRES-DR
The convergence of the restarted GMRES method can be significantly improved, for some problems, by using a weighted inner product that changes at each restart. How does this weighting affect convergence, and when is it useful? We show that weighted inner products can help in two distinct ways: when the coefficient matrix has localized eigenvectors, weighting can allow restarted GMRES to focus o...
متن کاملSome observations on the l2 convergence of the additive Schwarz preconditioned GMRES method
Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence result is available only in the energy norm (or the equivalent Sobolev H 1 norm). Very little progress has been made in the theoretical understandi...
متن کاملSome Observations on the L Convergence of the Additive Schwarz Preconditioned Gmres Method
Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence theory is available only in the energy norm (or the equivalent Sobolev H norm). Very little progress has been made in the theoretical understanding...
متن کاملSome Results on Weighted Cumulative Entropy
Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, Misagh et al. (2011) proposed a weighted information which is based on the cumulative entropy called Weighted Cumulative Entropy (WCE). The above-mentioned model is a Shiftdependent Uncertainty Measure. In this paper, we examine some of the properties of WCE and obtain some bounds for that. In order to ...
متن کاملSome Remarks on the Restarted and Augmented Gmres Method
Starting from the residual estimates for GMRES formulated by many authors, usually in terms of the quotient of the Hermitian part and the norm of a matrix or by using the field of values of a matrix, we present more general estimates which hold also for restarted and augmented GMRES. Sufficient conditions for convergence are formulated. All estimates are independent on the choice of an initial ...
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ژورنال
عنوان ژورنال: Numerical Algorithms
سال: 2014
ISSN: 1017-1398,1572-9265
DOI: 10.1007/s11075-013-9820-x