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522
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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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 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, the nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.
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 477 (30 self)
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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 time consuming process. The work described here can help in automating much of this process. We will concentrate our e orts on the widely used linear algebra kernels called the Basic Linear Algebra Subroutines (BLAS). In particular, the work presented here is for general matrix multiply, DGEMM. However 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.
NetSolve: A Network Server for Solving Computational Science Problems
 The International Journal of Supercomputer Applications and High Performance Computing
, 1995
"... This paper presents a new system, called NetSolve, that allows users to access computational resources, such as hardware and software, distributed across the network. This project has been motivated by the need for an easytouse, efficient mechanism for using computational resources remotely. Ease ..."
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Cited by 305 (32 self)
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This paper presents a new system, called NetSolve, that allows users to access computational resources, such as hardware and software, distributed across the network. This project has been motivated by the need for an easytouse, efficient mechanism for using computational resources remotely. Ease of use is obtained as a result of different interfaces, some of which do not require any programming effort from the user. Good performance is ensured by a loadbalancing policy that enables NetSolve to use the computational resource available as efficiently as possible. NetSolve is designed to run on any heterogeneous network and is implemented as a faulttolerant clientserver application. Keywords Distributed System, Heterogeneity, Load Balancing, ClientServer, Fault Tolerance, Linear Algebra, Virtual Library. University of Tennessee  Technical report No cs95313 Department of Computer Science, University of Tennessee, TN 37996 y Mathematical Science Section, Oak Ridge National La...
Optimizing Matrix Multiply using PHiPAC: a Portable, HighPerformance, ANSI C Coding Methodology
, 1996
"... Modern microprocessors can achieve high performance on linear algebra kernels but this currently requires extensive machinespecific hand tuning. We have developed a methodology whereby nearpeak performance on a wide range of systems can be achieved automatically for such routines. First, by analyz ..."
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Cited by 262 (24 self)
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Modern microprocessors can achieve high performance on linear algebra kernels but this currently requires extensive machinespecific hand tuning. We have developed a methodology whereby nearpeak performance on a wide range of systems can be achieved automatically for such routines. First, by analyzing current machines and C compilers, we've developed guidelines for writing Portable, HighPerformance, ANSI C (PHiPAC, pronounced "feepack"). Second, rather than code by hand, we produce parameterized code generators. Third, we write search scripts that and the best parameters for a given system. We report on a BLAS GEMM compatible multilevel cacheblocked matrix multiply generator which produces code that achieves around 90% of peak on the Sparcstation20/61, IBM RS/6000590, HP 712/80i, SGI Power Challenge R8k, and SGI Octane R10k, and over 80% of peak on the SGI Indigo R4k. The resulting routines are competitive with vendoroptimized BLAS GEMMs.
ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods.
, 1997
"... this document is intended to provide a cursory overview of the Implicitly Restarted Arnoldi/Lanczos Method that this software is based upon. The goal is to provide some understanding of the underlying algorithm, expected behavior, additional references, and capabilities as well as limitations of the ..."
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Cited by 215 (18 self)
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this document is intended to provide a cursory overview of the Implicitly Restarted Arnoldi/Lanczos Method that this software is based upon. The goal is to provide some understanding of the underlying algorithm, expected behavior, additional references, and capabilities as well as limitations of the software. 1.7 Dependence on LAPACK and BLAS
Pointbased POMDP algorithms: Improved analysis and implementation
 in Proceedings of Uncertainty in Artificial Intelligence
"... Existing complexity bounds for pointbased POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our conclusions may help guide future algorithm design. We also ..."
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Cited by 154 (3 self)
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Existing complexity bounds for pointbased POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our conclusions may help guide future algorithm design. We also discuss recent improvements to our (pointbased) heuristic search value iteration algorithm. Our new implementation calculates tighter initial bounds, avoids solving linear programs, and makes more effective use of sparsity. Empirical results show speedups of more than two orders of magnitude. 1
An UnsymmetricPattern Multifrontal Method for Sparse LU Factorization
 SIAM J. MATRIX ANAL. APPL
, 1994
"... Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops ..."
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Cited by 150 (27 self)
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Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily on dense matrix kernels exists for matrices whose pattern is very unsymmetric. We address this deficiency and present a new unsymmetricpattern multifrontal method based on dense matrix kernels. As in the classical multifrontal method, advantage is taken of repetitive structure in the matrix by factorizing more than one pivot in each frontal matrix thus enabling the use of Level 2 and Level 3 BLAS. The performance is compared with the classical multifrontal method and other unsymmetric solvers on a CRAY YMP.
An overview of the trilinos project
 ACM Transactions on Mathematical Software
"... The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundament ..."
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Cited by 143 (17 self)
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The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an objectoriented framework for the solution of largescale, complex multiphysics engineering and scientific problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. Trilinos uses a twolevel software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common lookandfeel, including configuration, documentation, licensing, and bugtracking. Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software. Sandia is a multiprogram laboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department of Energy under Contract DEAC0494AL85000. Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and
Intlab  Interval Laboratory
"... . INTLAB is a Matlab toolbox supporting real and complex interval scalars, vectors, and matrices, as well as sparse real and complex interval matrices. It is designed to be very fast. In fact, it is not much slower than the fastest pure floating point algorithms using the fastest compilers available ..."
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Cited by 131 (12 self)
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. INTLAB is a Matlab toolbox supporting real and complex interval scalars, vectors, and matrices, as well as sparse real and complex interval matrices. It is designed to be very fast. In fact, it is not much slower than the fastest pure floating point algorithms using the fastest compilers available (the latter, of course, without verification of the result). Portability is assured by implementing all algorithms in Matlab itself with exception of exactly three routines for switching the rounding downwards, upwards and to nearest. Timing comparisons show that the used concept achieves the anticipated speed with identical code on a variety of computers, ranging from PC's to parallel computers. INTLAB may be freely copied from our home page. 1. Introduction. The INTLAB concept splits into two parts. First, a new concept of a fast interval library is introduced. The main advantage (and difference to existing interval libraries) is that identical code can be used on a variety of computer a...