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4,191
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 773 (23 self)
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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
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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Neumann used the same name for Hilbert spaces in the modern sense (complete inner product spaces), which he defined in 1928. p. 3 line6: At the end of the line, 2ɛ should be 4ɛ. p. 3 I.1.2.3: The statement that a dense subspace of a Hilbert space H contains an orthonormal basis for H can be false if H
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 523 (68 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Automatically tuned linear algebra software
 CONFERENCE ON HIGH PERFORMANCE NETWORKING AND COMPUTING
, 1998
"... This paper describes an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. The production of such software for machines ranging from desktop workstations to embedded processors can be a tedious and ..."
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Cited by 478 (26 self)
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much ofthe technology and approach developed here can be applied to the other Level 3 BLAS and the general strategy can have an impact on basic linear algebra operations in general and may be extended to other important kernel operations.
Efficient and Practical Stochastic Subgradient Descent for Nuclear Norm Regularization
"... We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining lowrank stochastic subgradients with efficient incremental SVD updates, made possible by ..."
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Cited by 10 (0 self)
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by highly optimized and parallelizable dense linear algebra operations on small matrices. Our practical algorithms always maintain a lowrank factorization of iterates that can be conveniently held in memory and efficiently multiplied to generate predictions in matrix completion settings. Empirical
ASCENT: Adaptive selfconfiguring sensor networks topologies
, 2004
"... Advances in microsensor and radio technology will enable small but smart sensors to be deployed for a wide range of environmental monitoring applications. The low pernode cost will allow these wireless networks of sensors and actuators to be densely distributed. The nodes in these dense networks w ..."
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Cited by 449 (15 self)
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Advances in microsensor and radio technology will enable small but smart sensors to be deployed for a wide range of environmental monitoring applications. The low pernode cost will allow these wireless networks of sensors and actuators to be densely distributed. The nodes in these dense networks
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 324 (9 self)
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for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism
Benchmarking GPUs to tune dense linear algebra
, 2008
"... We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80–90 % of the pe ..."
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Cited by 242 (2 self)
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We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80
PEAS: A Robust Energy Conserving Protocol for Longlived Sensor Networks
, 2003
"... In this paper we present PEAS, a robust energyconserving protocol that can build longlived, resilient sensor networks using a very large number of small sensors with short battery lifetime. PEAS extends the network lifetime by maintaining a necessary set of working nodes and turning o redundant one ..."
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Cited by 349 (5 self)
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ones. PEAS operations are based on individual node's observation of the local environment and do not require any node to maintain per neighbor node state. PEAS performance possesses a high degree of robustness in the presence of both node power depletions and unexpected failures. Our simulations
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
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Cited by 314 (22 self)
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/Boeing collection of matrices for which we provide a number of tools. Among other things the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, performing basic linear algebra operations with sparse matrices and so on. Work done partly
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