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EQUATIONS WITH PRECONDITIONED KRYLOV SUBSPACE METHODS
"... Abstract. In this report, using SEPRAN [1], the incompressible Stokes and Navier Stokes problems are solved in a square and Lshaped domain with a varying grid size and Reynolds number. Both problems are solved with iterative solvers using an ILU preconditioner. Different ordering techniques of the ..."
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of the grid points and the unknowns are used to avoid breakdown of the LU decomposition. These ordering techniques used with ILU preconditioning makes that the iterative methods applied to the system of equations converge rapidly. With the reordering techniques, a direct solver can be used to solve
A theoretical overview of Krylov subspace methods
, 1995
"... We survey Krylov subspace methods for the solution of linear systems with focus on commonly used and recently developed methods. The approach is theoretical and complementary to the engineeringbased first article of this special issue. In particular convergence results are derived from a general th ..."
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Cited by 4 (0 self)
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We survey Krylov subspace methods for the solution of linear systems with focus on commonly used and recently developed methods. The approach is theoretical and complementary to the engineeringbased first article of this special issue. In particular convergence results are derived from a general
Nonlinear problems in analysis of Krylov subspace methods
"... convergence, spectral decomposition, numerical stability and rounding error analysis Consider a system of linear algebraic equations Ax = b where A is an n by n real matrix and b a real vector of length n. Unlike in the linear iterative methods based on the idea of splitting of A, the Krylov subspac ..."
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is linear, Krylov subspace methods are not. Their convergence behaviour cannot be viewed as an (unimportant) initial transient stage followed by the subsequent convergence stage. Apart from very simple, and from the point of view of Krylov subspace methods uninteresting cases, it cannot be meaningfully
Overview of Krylov subspace methods with applications to control problems
, 1990
"... This paper gives an overview of projection methods based on Krylov subspaces with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Spanfv; Av; : : : ; A m\Gamma1 vg, a ..."
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This paper gives an overview of projection methods based on Krylov subspaces with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Spanfv; Av; : : : ; A m\Gamma1 vg
Preconditioned Krylov Subspace Methods for Transport Equations
 Proceedings XENFIR III, Aguas de Lind'oia
, 1995
"... Transport equations have many important applications. Because the equations are based on highly nonnormal operators, they present difficulties in numerical computations. The iterative methods have been shown to be one of efficient numerical methods to solve transport equations. However, because of ..."
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of the nature of transport problems, convergence of iterative methods tends to slow for many important problems. In this paper, we focus on the development of algorithms to accelerate iterative methods. We investigate the applicability and performance of some Krylov subspace methods with preconditioners
Waveform Krylov Subspace Methods for Tightly Coupled Systems
"... We extend Krylov subspace methods, which are intended for iterative solution of systems of linear equations, to a function space for the solution of cicuit problems. Four of the previously untried methods are applied to a tightly coupled circuit to illustrate the convergence properties of these meth ..."
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We extend Krylov subspace methods, which are intended for iterative solution of systems of linear equations, to a function space for the solution of cicuit problems. Four of the previously untried methods are applied to a tightly coupled circuit to illustrate the convergence properties
The extended Krylov subspace method and orthogonal Laurent polynomials
 Miroslav S. Pranić, Lothar Reichel
"... Dedicated to Henk van der Vorst on the occasion of his 65th birthday. Abstract. The need to evaluate expressions of the form f(A)v, where A is a large sparse or structured symmetric matrix, v is a vector, and f is a nonlinear function, arises in many applications. The extended Krylov subspace method ..."
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Cited by 8 (2 self)
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method can be an attractive scheme for computing approximations of such expressions. This method projects the approximation problem onto an extended Krylov subspace K ℓ,m (A) = span{A −ℓ+1 v,..., A −1 v, v, Av,..., A m−1 v} of fairly small dimension, and then solves the small approximation problem so
Truncation Strategies For Optimal Krylov Subspace Methods
 SIAM J. Numer. Anal
, 1999
"... Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become excessiv ..."
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Cited by 47 (7 self)
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Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become
Geometric Aspects in the Theory of Krylov Subspace Methods
 Acta Numerica
, 1999
"... The recent development of Krylov subspace methods for the solution of operator equations has shown that two basic construction principles, the orthogonal residual (OR) and minimal residual (MR) approaches, underlie the most commonly used algorithms. It is shown that these can both be formulated ..."
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Cited by 42 (2 self)
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The recent development of Krylov subspace methods for the solution of operator equations has shown that two basic construction principles, the orthogonal residual (OR) and minimal residual (MR) approaches, underlie the most commonly used algorithms. It is shown that these can both be formulated
Flexible innerouter Krylov subspace methods
 SIAM J. NUMER. ANAL
, 2003
"... Flexible Krylov methodsrefersto a classof methodswhich accept preconditioning that can change from one step to the next. Given a Krylov subspace method, such as CG, GMRES, QMR, etc. for the solution of a linear system Ax = b, instead of having a fixed preconditioner M and the (right) preconditione ..."
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Cited by 34 (2 self)
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Flexible Krylov methodsrefersto a classof methodswhich accept preconditioning that can change from one step to the next. Given a Krylov subspace method, such as CG, GMRES, QMR, etc. for the solution of a linear system Ax = b, instead of having a fixed preconditioner M and the (right
Results 11  20
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164,712