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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 519 (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.
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 760 (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
Krogh, Basic Linear Algebra Subprograms for
"... Most numerical programs do similar operations 90 % time is at 10 % of the code If these 10 % of the code is optimized, programs will be fast Frequently used subroutines should be available For numerical computations, common operations can be easily identified Example: ..."
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Most numerical programs do similar operations 90 % time is at 10 % of the code If these 10 % of the code is optimized, programs will be fast Frequently used subroutines should be available For numerical computations, common operations can be easily identified Example:
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 469 (26 self)
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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
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 645 (21 self)
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gradient algorithms, indicating that I~QR is the most reliable algorithm when A is illconditioned. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: ApprorJmationleast squares approximation; G.1.3 [Numerical Analysis]: Numerical Linear Algebralinear systems (direct and
Multivariable Feedback Control: Analysis
 span (B∗) und Basis B∗ = { ω1
, 2005
"... multiinput, multioutput feedback control design for linear systems using the paradigms, theory, and tools of robust control that have arisen during the past two decades. The book is aimed at graduate students and practicing engineers who have a basic knowledge of classical control design and st ..."
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Cited by 533 (24 self)
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and statespace control theory for linear systems. A basic knowledge of matrix theory and linear algebra is required to appreciate and digest the material offered. This edition is a revised and expanded version of the first edition, which was published in 1996. The size of the
Basic linear algebra communication subprograms: Analysis and . . .
, 1994
"... The BLACS (Basic Linear Algebra Communication Subprograms) project is an ongoing investigation whose purpose is to create a linear algebra oriented message passing interface that is implemented efficiently and uniformly across a large range of distributed memory platforms. The length of time requir ..."
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Cited by 17 (6 self)
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The BLACS (Basic Linear Algebra Communication Subprograms) project is an ongoing investigation whose purpose is to create a linear algebra oriented message passing interface that is implemented efficiently and uniformly across a large range of distributed memory platforms. The length of time
An Updated Set of Basic Linear Algebra Subprograms (BLAS)
 ACM Transactions on Mathematical Software
, 2001
"... This paper summarizes the BLAS Technical Forum Standard, a speci #cation of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS. The complete standard can be found in #1#, and on the BLAS Technical Forum webpage #http: ..."
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Cited by 116 (7 self)
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This paper summarizes the BLAS Technical Forum Standard, a speci #cation of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS. The complete standard can be found in #1#, and on the BLAS Technical Forum webpage #http:##www.netlib.org#blas#blastforum##
A set of Level 3 Basic Linear Algebra Subprograms for sparse matrices
 ACM Trans. Math. Softw
, 1995
"... This paper proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. We discuss the design, implementation and use of subprograms for the multiplication of a full matrix by a sparse one and for the solution of sparse triangular systems with one or more ..."
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Cited by 38 (8 self)
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This paper proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. We discuss the design, implementation and use of subprograms for the multiplication of a full matrix by a sparse one and for the solution of sparse triangular systems with one
The Basic Polynomial Algebra Subprograms
"... Abstract. The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [10] targeting multicore proce ..."
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Abstract. The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [10] targeting mul
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