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Spectral deflation in Krylov solvers: A theory of coordinate space based methods
 ETNA
"... Abstract. For the iterative solution of large sparse linear systems we develop a theory for a family of augmented and deflated Krylov space solvers that are coordinate based in the sense that the given problem is transformed into one that is formulated in terms of the coordinates with respect to the ..."
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Cited by 4 (1 self)
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Abstract. For the iterative solution of large sparse linear systems we develop a theory for a family of augmented and deflated Krylov space solvers that are coordinate based in the sense that the given problem is transformed into one that is formulated in terms of the coordinates with respect
Parallel LagrangeNewtonKrylovSchur methods for PDEconstrained optimization. Part I: The KrylovSchur solver
 SIAM J. SCI. COMPUT
, 2000
"... Large scale optimization of systems governed by partial differential equations (PDEs) is a frontier problem in scientific computation. The stateoftheart for such problems is reduced quasiNewton sequential quadratic programming (SQP) methods. These methods take full advantage of existing PDE so ..."
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Cited by 113 (18 self)
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solver technology and parallelize well. However, their algorithmic scalability is questionable; for certain problem classes they can be very slow to converge. In this twopart article we propose a new method for steadystate PDEconstrained optimization, based on the idea of full space SQP with reduced
Deflated and augmented Krylov subspace methods: A framework for deflated . . .
, 2013
"... We present an extension of the framework of Gaul et al. (SIAM J. Matrix Anal. Appl. 34, 495–518 (2013)) for deflated and augmented Krylov subspace methods satisfying a Galerkin condition to more general Petrov–Galerkin conditions. The main goal is to apply the framework also to the biconjugate gra ..."
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Cited by 12 (2 self)
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generate a Krylov space for a singular operator that is associated with the projected problem. The deflated biconjugate gradient requires two such Krylov spaces, but it also allows us to solve two dual linear systems at once. Deflated Lanczostype product methods fit in our new framework too. The question
Krylov space solvers for shifted linear systems
, 1996
"... We investigate the application of Krylov space methods to the solution of shifted linear systems of the form (A + σ)x − b = 0 for several values of σ simultaneously, using only as many matrixvector operations as the solution of a single system requires. We find a suitable description of the problem ..."
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We investigate the application of Krylov space methods to the solution of shifted linear systems of the form (A + σ)x − b = 0 for several values of σ simultaneously, using only as many matrixvector operations as the solution of a single system requires. We find a suitable description
Acceleration of Preconditioned Krylov Solvers for Bubbly Flow Problems
"... Abstract. We consider the linear system which arises from discretization of the pressure Poisson equation with Neumann boundary conditions, coming from bubbly flow problems. In literature, preconditioned Krylov iterative solvers are proposed, but these show slow convergence for relatively large an ..."
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Abstract. We consider the linear system which arises from discretization of the pressure Poisson equation with Neumann boundary conditions, coming from bubbly flow problems. In literature, preconditioned Krylov iterative solvers are proposed, but these show slow convergence for relatively large
Deflation based preconditioning of linear systems of equations
"... For most realworld problems Krylov space solvers only converge in a reasonable number of iterations if a suitable preconditioning technique is applied. This is particularly true for problems where the linear operator has eigenvalues of small absolute value — a situation that is very common in pract ..."
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For most realworld problems Krylov space solvers only converge in a reasonable number of iterations if a suitable preconditioning technique is applied. This is particularly true for problems where the linear operator has eigenvalues of small absolute value — a situation that is very common
1. SUOM: A NEW OPTIMAL KRYLOV SOLVER
, 2004
"... In this paper I describe a new optimal Krylov subspace solver for shifted unitary matrices called the Shifted Unitary Orthogonal Method (SUOM). This algorithm is used as a benchmark against any improvement like the twogrid algorithm. I use the latter to show that the overlap operator can be inverte ..."
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In this paper I describe a new optimal Krylov subspace solver for shifted unitary matrices called the Shifted Unitary Orthogonal Method (SUOM). This algorithm is used as a benchmark against any improvement like the twogrid algorithm. I use the latter to show that the overlap operator can
Flexible GMRES with deflated restarting
 SIAM J. Scientific Computing
, 2009
"... Abstra t. In many situations, it has been observed that signi
ant
onvergen
e improvements
an be a
hieved in pre
onditioned Krylov subspa
e methods by enri
hing them with some spe
tral information. On the other hand ee tive pre
onditioning strategies are often designed where the pre
onditioner va ..."
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Cited by 8 (4 self)
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varies from one step to the next so that a exible Krylov solver is required. In this paper, we present a new numeri
al te
hnique for nonsymmetri problems that
ombines these two features. We illustrate the numeri
al behavior of the new solver both on a set of small a
ademi
test examples as well
Accuracy Of Two ThreeTerm And Three TwoTerm Recurrences For Krylov Space Solvers
, 1999
"... . It has been widely observed that Krylov space solvers based on two threeterm recurrences can give signicantly less accurate residuals than mathematically equivalent solvers implemented with three twoterm recurrences. In this paper we attempt to clarify and justify this dierence theoretically by ..."
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Cited by 18 (8 self)
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. It has been widely observed that Krylov space solvers based on two threeterm recurrences can give signicantly less accurate residuals than mathematically equivalent solvers implemented with three twoterm recurrences. In this paper we attempt to clarify and justify this dierence theoretically
Results 1  10
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