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Krylov subspace methods on supercomputers
 SIAM J. SCI. STAT. COMPUT
, 1989
"... This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three dimensional model ..."
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Cited by 79 (4 self)
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This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three dimensional
Local Operators In Krylov Subspaces
"... . For a bounded linear operator A on a Hilbert space H we study local spectral sets and their relation to the spectrum of the local operator. By the local operator we mean A restricted to a Krylov subspace spanfb; Ab; A 2 b; :::g for a generic b 2 H. Moreover we investigate the relation between oe ..."
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. For a bounded linear operator A on a Hilbert space H we study local spectral sets and their relation to the spectrum of the local operator. By the local operator we mean A restricted to a Krylov subspace spanfb; Ab; A 2 b; :::g for a generic b 2 H. Moreover we investigate the relation between
Krylov Subspace Methods for . . .
, 2007
"... Topology optimization is a powerful tool for global and multiscale design of structures, microstructures, and materials. The computational bottleneck of topology optimization is the solution of a large number of extremely illconditioned linear systems arising in the finite element analysis. Adaptiv ..."
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. Adaptive mesh refinement (AMR) is one efficient way to reduce the computational cost. We propose a new AMR scheme for topology optimization that results in more robust and efficient solutions. For large sparse symmetric linear systems arising in topology optimization, Krylov subspace methods are required
Krylov Subspace Estimation
, 2000
"... . Computing the linear leastsquares estimate of a highdimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system efficiently using a Krylov subspace method, such as the conjugate gradient (CG) algorithm. Computing ..."
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Cited by 20 (3 self)
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. Computing the linear leastsquares estimate of a highdimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system efficiently using a Krylov subspace method, such as the conjugate gradient (CG) algorithm
Deflated and augmented Krylov subspace techniques
 Numer. Linear Algebra Appl
, 1996
"... We present a general framework for a number of techniques based on projection methods on `augmented Krylov subspaces'. These methods include the deflated GMRES algorithm, an innerouter FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often ..."
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Cited by 73 (11 self)
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We present a general framework for a number of techniques based on projection methods on `augmented Krylov subspaces'. These methods include the deflated GMRES algorithm, an innerouter FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods
Krylov subspace methods in the electronic industry
, 2004
"... Summary. Krylov subspace methods are wellknown for their nice properties, but they have to be implemented with care. In this article the mathematical consequences encountered during implementation of Krylov subspace methods in an existing layoutsimulator are discussed. Briefly, the representation ..."
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Summary. Krylov subspace methods are wellknown for their nice properties, but they have to be implemented with care. In this article the mathematical consequences encountered during implementation of Krylov subspace methods in an existing layoutsimulator are discussed. Briefly
KRYLOV SUBSPACE ACCELERATION OF WAVEFORM RELAXATION ∗
"... Abstract. In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving timedependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution v ..."
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Cited by 2 (0 self)
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Abstract. In this paper we describe and analyze Krylov subspace techniques for accelerating the convergence of waveform relaxation for solving timedependent problems. A new class of accelerated waveform methods, convolution Krylov subspace methods, is presented. In particular, we give convolution
Analysis of Augmented Krylov Subspace Methods
 SIAM J. Matrix Anal. Appl
, 1995
"... Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form Km + W, where Km is the standard Krylov subspace associated with the original linear system, and W is some other subspace. These `augmented Krylov subspace methods' incl ..."
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Residual norm estimates are derived for a general class of methods based on projection techniques on subspaces of the form Km + W, where Km is the standard Krylov subspace associated with the original linear system, and W is some other subspace. These `augmented Krylov subspace methods
Krylov Subspace Methods on Parallel Computers
, 1996
"... The aspects of implementing Krylov subspace methods on parallel computers are investigated. It is shown how to increase the parallel performance by restructuring standard sequential versions of the algorithms, with some tradeoff in stability. Further, we discuss how the computational kernels in Kry ..."
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The aspects of implementing Krylov subspace methods on parallel computers are investigated. It is shown how to increase the parallel performance by restructuring standard sequential versions of the algorithms, with some tradeoff in stability. Further, we discuss how the computational kernels
Results 1  10
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1,089