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369,099
Preconditioning Parallel Multisplittings for Solving Linear Systems of Equations ChiouMing
, 1992
"... We consider the practical implementation of Krylov subspace methods (conjugate gradients, GMRES, etc.) for parallel computers in the case where the preconditioning matrix is a multisplitting. The algorithm can be efficiently implemented by dividing the work into tasks that generate search directions ..."
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We consider the practical implementation of Krylov subspace methods (conjugate gradients, GMRES, etc.) for parallel computers in the case where the preconditioning matrix is a multisplitting. The algorithm can be efficiently implemented by dividing the work into tasks that generate search
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 766 (23 self)
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illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
 SIAM J. SCI. STAT. COMPUT
, 1986
"... We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered a ..."
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Cited by 2046 (40 self)
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We present an iterative method for solving linear systems, which has the property ofminimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an l2orthogonal basis of Krylov subspaces. It can be considered
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 649 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 568 (23 self)
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for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds
The nas parallel benchmarks
 The International Journal of Supercomputer Applications
, 1991
"... A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers. These benchmarks consist of ve \parallel kernel " benchmarks and three \simulated application" benchmarks. Together they mimic the computation and data movement characterist ..."
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Cited by 686 (10 self)
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benchmarking approaches on highly parallel systems are avoided. 1
Parallel database systems: the future of high performance database systems
 Communications of the ACM
, 1992
"... Abstract: Parallel database machine architectures have evolved from the use of exotic hardware to a software parallel dataflow architecture based on conventional sharednothing hardware. These new designs provide impressive speedup and scaleup when processing relational database queries. This paper ..."
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Cited by 638 (13 self)
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Abstract: Parallel database machine architectures have evolved from the use of exotic hardware to a software parallel dataflow architecture based on conventional sharednothing hardware. These new designs provide impressive speedup and scaleup when processing relational database queries. This paper
Cognitive load during problem solving: effects on learning
 COGNITIVE SCIENCE
, 1988
"... Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill. Evidence that conventional problemsolving activity is not effective in schema acquisition is also accumulating. It is suggested t ..."
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Cited by 603 (13 self)
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Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill. Evidence that conventional problemsolving activity is not effective in schema acquisition is also accumulating. It is suggested
Results 1  10
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