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Fast Nonsymmetric Iterations and Preconditioning for NavierStokes Equations
 SIAM J. Sci. Comput
, 1994
"... Discretization and linearization of the steadystate NavierStokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded i ..."
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Cited by 74 (10 self)
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Discretization and linearization of the steadystate NavierStokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization. We confirm and supplement these analytic results with a series of numerical experiments indicating that Krylov subspace iterative methods for nonsymmetric systems display rates of convergence that are independent of the mesh parameter. In addition, we show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner. * This work was supported by the U. S. Army Research Office under grant DAAL0392G0016 and the U. S. National Science Foundation under grant ASC8958544 at the University of Maryland, and the Science and Engineering Research Council of Great Britain V...
On the Powers of a Matrix with Perturbations
, 2001
"... Let A be a matrix of order n. The properties of the powers A k of A have been extensively studied in the literature. This paper concerns the perturbed powers P k = (A + E k )(A + E k\Gamma1 ) \Delta \Delta \Delta (A + E 1 ); where the E k are perturbation matrices. We will treat three problems co ..."
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Cited by 2 (0 self)
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Let A be a matrix of order n. The properties of the powers A k of A have been extensively studied in the literature. This paper concerns the perturbed powers P k = (A + E k )(A + E k\Gamma1 ) \Delta \Delta \Delta (A + E 1 ); where the E k are perturbation matrices. We will treat three problems concerning the asymptotic behavior of the perturbed powers. First, determine conditions under which P k ! 0. Second, determine the limiting structure of P k . Third, investigate the convergence of the power method with error: that is, given u 1 , determine the behavior of u k = k P k u 1 , where k is a suitable scaling factor.
Resolvent estimates of Carleman type and an application to the Perturbation Of Spectra
, 2002
"... Let A belong to the Schattenvon Neumann ideal S p for 0 < p < 1. We give an upper bound for the operator norm of the resolvent (zI A) of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausd ..."
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Let A belong to the Schattenvon Neumann ideal S p for 0 < p < 1. We give an upper bound for the operator norm of the resolvent (zI A) of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to S p .