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Software libraries for linear algebra computations on high performance computers
 SIAM REVIEW
, 1995
"... This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed b ..."
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Cited by 67 (16 self)
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This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of blockpartitioned algorithms in reducing the frequency of data movement between different levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subprograms (BLAS) as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms (BLACS) as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct highe...
PUMMA: Parallel Universal Matrix Multiplication Algorithms on Distributed Memory Concurrent Computers
, 1993
"... 05, NASA Ames Research Center, Moffet Field, CA 94035 134. William C. Skamarock, 3973 Escuela Court, Boulder, CO 80301 135. Richard Smith, Los Alamos National Laboratory, Group T3, Mail Stop B2316, Los Alamos, NM 87545 136. Peter Smolarkiewicz, National Center for Atmospheric Research, MMM Group, ..."
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Cited by 59 (10 self)
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05, NASA Ames Research Center, Moffet Field, CA 94035 134. William C. Skamarock, 3973 Escuela Court, Boulder, CO 80301 135. Richard Smith, Los Alamos National Laboratory, Group T3, Mail Stop B2316, Los Alamos, NM 87545 136. Peter Smolarkiewicz, National Center for Atmospheric Research, MMM Group, P. O. Box 3000, Boulder, CO 80307 137. Jurgen Steppeler, DWD, Frankfurterstr 135, 6050 Offenbach, WEST GERMANY 138. Rick Stevens, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439 139. Paul N. Swarztrauber, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307 140. Wei Pai Tang, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 141. Harold Trease, Los Alamos National Laboratory, Mail Stop B257, Los Alamos, NM 87545 142. Robert G. Voigt, ICASE, MS 132C, NASA Langley Research Center, Hampton, VA 23665 143. Mary F. Wheeler, Rice University, Department of Mathematical Sc
The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and Bidiagonal Form
, 1995
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Public international benchmarks for parallel computers, parkbench committee reportâ€™, Sci
 Program
, 1994
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Interoperability of Data Parallel Runtime Libraries with MetaChaos
 In Proceedings of the Eleventh International Parallel Processing Symposium. IEEE Computer
, 1997
"... This paper describes a framework for providing the ability to use multiple specialized data parallel libraries and/or languages within a single application. The ability to use multiple libraries is required in many application areas, such as multidisciplinary complex physical simulations and remote ..."
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Cited by 27 (11 self)
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This paper describes a framework for providing the ability to use multiple specialized data parallel libraries and/or languages within a single application. The ability to use multiple libraries is required in many application areas, such as multidisciplinary complex physical simulations and remote sensing image database applications. An application can consist of one program or multiple programs that use different libraries to parallelize operations on distributed data structures. The framework is embodied in a runtime library called Meta Chaos that has been used to exchange data between data parallel programs written using High Performance Fortran, the Chaos and Multiblock Parti libraries developed at Maryland for handling various types of unstructured problems, and the runtime library for pC++, a data parallel version of C++ from Indiana University. Experimental results show that MetaChaos is able to move data between libraries efficiently, and that MetaChaos provides effective ...
Scalability Issues Affecting the Design of a Dense Linear Algebra Library
 JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
, 1994
"... This paper discusses the scalability of Cholesky, LU, and QR factorization routines on MIMD distributed memory concurrent computers. These routines form part of the ScaLAPACK mathematical software library that extends the widelyused LAPACK library to run efficiently on scalable concurrent computers ..."
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Cited by 24 (12 self)
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This paper discusses the scalability of Cholesky, LU, and QR factorization routines on MIMD distributed memory concurrent computers. These routines form part of the ScaLAPACK mathematical software library that extends the widelyused LAPACK library to run efficiently on scalable concurrent computers. To ensure good scalability and performance, the ScaLAPACK routines are based on blockpartitioned algorithms that reduce the frequency of data movement between different levels of the memory hierarchy, and particularly between processors. The block cyclic data distribution, that is used in all three factorization algorithms, is described. An outline of the sequential and parallel blockpartitioned algorithms is given. Approximate models of algorithms' performance are presented to indicate which factors in the design of the algorithm have an impact upon scalability. These models are compared with timings results on a 128node Intel iPSC/860 hypercube. It is shown that the routines are highl...
Comparison of Scalable Parallel Matrix Multiplication Libraries
 in Proceedings of the Scalable Parallel Libraries Conference, Starksville, MS
, 1993
"... This paper compares two general library routines for performing parallel distributed matrix multiplication. The PUMMA algorithm utilizes block scattered data layout, whereas BiMMeR utilizes virtual 2D torus wrap. The algorithmic differences resulting from these different layouts are discussed as we ..."
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Cited by 17 (2 self)
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This paper compares two general library routines for performing parallel distributed matrix multiplication. The PUMMA algorithm utilizes block scattered data layout, whereas BiMMeR utilizes virtual 2D torus wrap. The algorithmic differences resulting from these different layouts are discussed as well as the general issues associated with different data layouts for library routines. Results on the Intel Delta for the two matrix multiplication algorithms are presented. 1. Introduction Matrix multiplication is a standard algorithm that is an important computational kernel in many applications including eigensolvers [3] and LU factorization [15]. Utilizing matrix multiplication is one of the principal ways of achieving high efficiency block algorithms in packages such as LAPACK [2]. The BLAS 3 routines were added to achieve this block performance on computers, and optimized versions are available on most serial machines [10]. For matrix multiplication, the BLAS 3 routine XGEMM is availa...
The Design of Linear Algebra Libraries for High Performance Computers
, 1993
"... This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followe ..."
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Cited by 16 (1 self)
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This paper discusses the design of linear algebra libraries for high performance computers. Particular emphasis is placed on the development of scalable algorithms for MIMD distributed memory concurrent computers. A brief description of the EISPACK, LINPACK, and LAPACK libraries is given, followed by an outline of ScaLAPACK, which is a distributed memory version of LAPACK currently under development. The importance of blockpartitioned algorithms in reducing the frequency of data movementbetween di#erent levels of hierarchical memory is stressed. The use of such algorithms helps reduce the message startup costs on distributed memory concurrent computers. Other key ideas in our approach are the use of distributed versions of the Level 3 Basic Linear Algebra Subgrams #BLAS# as computational building blocks, and the use of Basic Linear Algebra Communication Subprograms #BLACS# as communication building blocks. Together the distributed BLAS and the BLACS can be used to construct ...