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A set of level 3 basic linear algebra subprograms

J. J. Dongarra, Jeremy Du Croz, Sven Hammarling, I. S. Duff
1990 ACM Transactions on Mathematical Software  
This paper describes a set of Level 3 Basic Linear Algebra Subprograms (Level 3 BLAS).  ...  The Level 3 BLAS are targeted at matrix-matrix operations, with the aim of providing more efficient, but portable, implementations of algorithms on high-performance computers, especially those with hierarchical  ...  ACKNOWLEDGMENTS Draft proposals for the Level 3 BLAS were discussed initially at a workshop at Argonne National Laboratory, on January [26] [27] 1987, and subsequently at various meetings.  ... 
doi:10.1145/77626.79170 fatcat:tbpnzmhwqjbe3mdakq2c4l5yny

Algorithm 679; a set of level 3 basic linear algebra subprograms: model implementation and test programs

J. J. Dongarra, Jermey Du Cruz, Sven Hammerling, I. S. Duff
1990 ACM Transactions on Mathematical Software  
This paper describes a model implementation and test software for the Level 3 Basic Linear Algebra Subprograms (Level 3 BLAS).  ...  The model implementation provides a portable set of Fortran 77 Level 3 BLAS for machines where specialized implementations do not exist or are not required.  ...  SCOPE OF THE ALGORITHM In [4] we have defined the specification of a set of Level 3 Basic Linear Algebra Subprograms for selected matrix-matrix operations.  ... 
doi:10.1145/77626.77627 fatcat:jlxh3oyu2jfyvasfz3cmyuqti4

Basic Linear Algebra Subprograms for Fortran Usage

C. L. Lawson, R. J. Hanson, D. R. Kincaid, F. T. Krogh
1979 ACM Transactions on Mathematical Software  
A package of 39 low-level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN.  ...  The subprograms and a test driver are available in portable FORTRAN.  ...  dot product by a unique mnemonic name. (3) Since a significant amount of the execution time in complicated linear algebraic programs may be spent in a few low-level operations, a reduction of execution  ... 
doi:10.1145/355841.355847 fatcat:dgmvoze2nncldfii6jymviv2di

ScaLAPACK tutorial [chapter]

Jack Dongarra, L. Susan Blackford
1996 Lecture Notes in Computer Science  
ScaLAPACK is a library of high performance linear algebra routines for distributed memory MIMD computers.  ...  We have been successful in attaining these goals, limiting most machine dependencies to two standard libraries called the BLAS, or Basic Linear Algebra Subroutines, and BLACS, or Basic Linear Algebra Communication  ...  Acknowledgments We wish to acknowledge Antoine Petitet for assembling the previous version of this tutorial, and thank him for his advice and contributions to this e ort.  ... 
doi:10.1007/3-540-62095-8_22 fatcat:uihvkuhlufhptemyfl3tugkhb4

Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs

Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson
1988 ACM Transactions on Mathematical Software  
This paper describes a model implementation and test software for the Level 2 Basic Linear Algebra Subprograms (Level 2 BLAS).  ...  The model implementation provides a portable set of FORTRAN 77 Level 2 BLAS for machines where specialized implementations do not exist or are not required.  ...  but increase or decrease Algorithm 656: An Extended Set of Basic Linear Algebra Subprograms 23 by 1 on each iteration of the outer loop.  ... 
doi:10.1145/42288.42292 fatcat:jh264nty7fbpnloe4642hxhsvq

ScaLAPACK tutorial [chapter]

Jack Dongarra, Antoine Petitet
1996 Lecture Notes in Computer Science  
The ScaLAPACK project is comprised of 4 components: dense matrix software (ScaLAPACK) large sparse eigenvalue software (PARPACK) sparse direct systems software (CAPSS) preconditioners for large sparse  ...  The Parallel Basic Linear Algebra Subprograms (PBLAS) PBLAS { INTRODUCTION Parallel Basic Linear Algebra Subprograms for distributed memory MIMD computers.  ...  BLAS Tutorial (lapack@cs.utk.edu), August 1996 8 BASIC LINEAR ALGEBRA SUBPROGRAMS (BLAS) Arithmetic is only performed at the top of the memory hierarchy, ) keep data as close as pos- sible to the  ... 
doi:10.1007/3-540-60902-4_20 fatcat:qetqnjf65ncztatiks4izbpc3y

Case studies on the development of ScaLAPACK and the NAG Numerical PVM Library [chapter]

J. J. Dongarra, S. Hammarling, A. Petitet
1997 IFIP Advances in Information and Communication Technology  
In this paper we look at the development of ScaLAPACK, a software library for dense and banded numerical linear algebra, and the NAG Numerical PVM Library, which includes software for dense and sparse  ...  linear algebra, quadrature, optimization and random number generation.  ...  of parallel software, for their valuable input.  ... 
doi:10.1007/978-1-5041-2940-4_18 fatcat:2wwpbtisdbgolkawxxwnbnpswq

A proposal for a set of parallel basic linear algebra subprograms [chapter]

Jaeyoung Choi, Jack Dongarra, Susan Ostrouchov, Antoine Petitet, David Walker, R. Clinton Whaley
1996 Lecture Notes in Computer Science  
This paper describes a proposal for a set of Parallel Basic Linear Algebra Subprograms PBLAS.  ...  This paper presents a reasonable set of adoptable solutions to successfully design and implement the Parallel Basic Linear Algebra Subprograms.  ...  Vol. 16 , no. 1, page 1 de ning and proposing a set of Level 3 Basic Linear Algebra Subprograms.  ... 
doi:10.1007/3-540-60902-4_13 fatcat:55xiy7xzqjamre6fk5ire2oaau

Page 2361 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
Other key ideas in our approach are the use of distributed versions of the Level 2 and Level 3 basic linear algebra subprograms (BLAS) as computational building blocks, and the use of basic linear algebra  ...  Summary: “We discuss the design of linear algebra libraries for high performance computers.  ... 

LAPACK95 - HIGH PERFORMANCE LINEAR ALGEBRA PACKAGE

J. Dongarra, J. Waśniewski
2000 Mathematical Modelling and Analysis  
LAPACK95 is a set of FORTRAN95 subroutines which interfaces FORTRAN95 with LAPACK.  ...  In both types of interfaces no distinction is made between single and double precision or between real and complex data types.  ...  LAPACK is designed at the outset to exploit the Level 3 BLAS { a set of speci cations for FORTRAN subprograms that do various types of matrix multiplication and the solution of triangular systems with  ... 
doi:10.3846/13926292.2000.9637127 fatcat:bsh27g3s5rhcbd5kqnk7o3p3ae

Standards for graph algorithm primitives

Tim Mattson, David Bader, Jon Berry, Aydin Buluc, Jack Dongarra, Christos Faloutsos, John Feo, John Gilbert, Joseph Gonzalez, Bruce Hendrickson, Jeremy Kepner, Charles Leiserson (+7 others)
2013 2013 IEEE High Performance Extreme Computing Conference (HPEC)  
It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive  ...  This paper is a position paper defining the problem and announcing our intention to launch an open effort to define this standard.  ...  RECOMENDATAION We believe the research community working on graph algorithms expressed as linear algebra should come together now and define a common API they can use in their research.  ... 
doi:10.1109/hpec.2013.6670338 dblp:conf/hpec/MattsonBBBDFFGGHKLLPPRSWY13 fatcat:zq2i4aa3njflhnvdvb5gghyru4

Datalog extension for nested relations

A. Benczúr, C. Hajas, G. Kovács
1995 Computers and Mathematics with Applications  
A nested Datalog program has a hierarchical structure of rules and subprograms to manipulate relation values of nested relations.  ...  Finally, we relate the expressive power of nonrecursive nested Datalog to the power of nested relational algebra and safe nested tuple relational calculus.  ...  expressed in the basic algebras.  ... 
doi:10.1016/0898-1221(95)00174-w fatcat:itb5yeimajbipkry23oscw5efa

BTAS: A Library for Tropical Algebra [article]

Ahsan Humayun, Dr.Muhammad Asif, Dr.Muhammmad Kashif Hanif
2017 arXiv   pre-print
In this paper we proposed and designed a library based on Tropical Algebra which is used to provide standard vector and matrix operations namely Basic Tropical Algebra Subroutines (BTAS).  ...  The developed library for tropical algebra delivered extensively better results on a less expensive GPU as compared to the same on CPU.  ...  Basic Linear Algebra Subprograms (BLAS are routines that offer standardized ingredients for executing basic vector and matrix operations.  ... 
arXiv:1701.04733v1 fatcat:3qf4zyllifbd5arsi7nokyzrc4

PB-BLAS: a set of parallel block basic linear algebra subprograms

Jaeyoung Choi, Jack J. Dongarra, David W. Walker
1996 Concurrency Practice and Experience  
The routines are referred to as block basic linear algebra subprograms (BLAS), and their use is restricted to computations in which one or more of the matrices involved consists of a single row or column  ...  This is particularly true for distributed memory machines, for which the block BLAS are referred to as the parallel block basic linear algebra subprograms (PB-BLAS).  ...  The first set of basic linear algebra subprograms (Level 1 BLAS) [2] defines operations on one or two vectors. LINPACK [3] and EISPACK [4] are built on top of the Level 1 BLAS.  ... 
doi:10.1002/(sici)1096-9128(199609)8:7<517::aid-cpe226>3.0.co;2-w fatcat:tiugqu2zi5cfxa4in5tkj4sfm4

Engineering and Scientific Subroutine Library for the IBM 3090 Vector Facility

J. McComb, S. Schmidt
1988 IBM Systems Journal  
A combination of matrix multiplication and addition, a proposed Level 3 BLAS," is also included. Linear algebraic equations.  ...  Hanson, “Preliminary Proposal for a Set of Level 3 BLAS,” presented at the Workshop on the Level 3 BLAS, Argonne National Laboratory, January 1987. 15.  ... 
doi:10.1147/sj.274.0404 fatcat:reqcrqlx75cazcq6mya5d6bdfy
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