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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 446 (70 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.
Future Research Directions In Problem Solving Environments For Computational Science
 Center for Supercomputing Research and Development
, 1991
"... this report was partially supported by Grant CCR9024549 from the National Science Foundation. This is a report to the National Science Foundation and other agencies; it is not a report by or of the National Science Foundation or any other agency. Participants at the Workshop on Research Directio ..."
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Cited by 18 (4 self)
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this report was partially supported by Grant CCR9024549 from the National Science Foundation. This is a report to the National Science Foundation and other agencies; it is not a report by or of the National Science Foundation or any other agency. Participants at the Workshop on Research Directions in Integrating Numerical Analysis, Symbolic Computing, Computational Geometry, and Artificial Intelligence for Computational Science Conference Organizers
On large scale diagonalization techniques for the Anderson model of localization
 SIAM REVIEW
, 2005
"... We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric indefinite matrices of the Anderson model of localization. We compar ..."
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Cited by 8 (6 self)
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We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shiftandinvert techniques in the implicitly restarted Lanczos method and in the JacobiDavidson method. Our preconditioning approaches for the shiftandinvert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDL T factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly illconditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerative the computation of a largescale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude.
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. ..."
Abstract

Cited by 3 (0 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.
Are There Iterative BLAS?
, 1994
"... A technique for optimizing software is proposed that involves the use of a standardized set of computational kernels that are common to many iterative methods for solving large sparse linear systems of equations. These kernels, referred to as "Iterative Basic Linear Algebra Subprograms" or "Iterativ ..."
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Cited by 3 (0 self)
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A technique for optimizing software is proposed that involves the use of a standardized set of computational kernels that are common to many iterative methods for solving large sparse linear systems of equations. These kernels, referred to as "Iterative Basic Linear Algebra Subprograms" or "Iterative BLAS", are defined and techniques for their optimization on vector computers are presented. Several sparse matrix storage formats for different classes of matrix problems are proposed that allow the vectorization of fundamental operations in various iterative methods using these kernels. 1 Introduction Many iterative methods perform operations that can be easily optimized on most vector computers, such as the dot product of two vectors and the updating of a vector using another vector. These operations are often used in linear algebra applications, and they have been denoted as Basic Linear Algebra Subprograms or BLAS [23]. In the BLAS library, the calling sequences of these primitive vec...
BLAS Technical Workshop
, 1995
"... The BLAS Technical Workshop was held on November 1314, 1995, in Knoxville, Tennessee. Its focus was on developing a set of Parallel BLAS and related interfaces for linear algebra, specifically the Sparse BLAS, Sparse PBLAS, BLACS, and extensions to the BLAS. Fiftytwo people were in attendance. Con ..."
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Cited by 2 (0 self)
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The BLAS Technical Workshop was held on November 1314, 1995, in Knoxville, Tennessee. Its focus was on developing a set of Parallel BLAS and related interfaces for linear algebra, specifically the Sparse BLAS, Sparse PBLAS, BLACS, and extensions to the BLAS. Fiftytwo people were in attendance. Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.1 Extensions to the existing BLAS : : : : : : : : : : : : : : : : : : : : 2 3 Sparse BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 4 Future Design Issues : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 4.1 Parallel BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4.2 Matrix Distribution : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4.3 Message Passing (Communication) : : : : : : : : : : : : : : : : : : : 9 5 Implementation Issues : : :...
LAPACK Working Note 109 BLAS Technical Workshop
"... The BLAS Technical Workshop was held on November 1314, 1995, in Knoxville, Tennessee. Its focus was on developing a set of Parallel BLAS and related interfaces for linear algebra, specifically the Sparse BLAS, Sparse PBLAS, BLACS, and extensions to the BLAS. Fiftytwo people were in attendance. Con ..."
Abstract
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The BLAS Technical Workshop was held on November 1314, 1995, in Knoxville, Tennessee. Its focus was on developing a set of Parallel BLAS and related interfaces for linear algebra, specifically the Sparse BLAS, Sparse PBLAS, BLACS, and extensions to the BLAS. Fiftytwo people were in attendance. Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.1 Extensions to the existing BLAS : : : : : : : : : : : : : : : : : : : : 2 3 Sparse BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 4 Future Design Issues : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 4.1 Parallel BLAS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4.2 Matrix Distribution : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 4.3 Message Passing (Communication) : : : : : : : : : : : : : : : : : : : 9 5 Implementation Issues : : : ...
Numerical Algorithms Group, Ltd. and
"... Subprograms (Level 2 BLAS). Level 2 BLAS are targeted at matrixvector operations with the aim of providing more efficient, but portable, implementations of algorithms on highperformance computers. The model implementation provides a portable set of FORTRAN 77 Level 2 BLAS for machines where speci ..."
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Subprograms (Level 2 BLAS). Level 2 BLAS are targeted at matrixvector operations with the aim of providing more efficient, but portable, implementations of algorithms on highperformance computers. 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. The test software aims to verify that specialized implementations meet the specification of Level 2 BLAS and that implementations are correctly installed. Categories and Subject Descriptors: F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problemscompututiotts on matrices; G.l.O [Numerical Analysis]: