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Index Terms

An updated set of basic linear algebra subprograms (BLAS)
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Linear algebra algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
  2. Mathematical software

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Reviews

Reviewer: Jesse Louis Barlow

The basic linear algebra subroutines (BLAS) have become an essential part of the development of numerical software in Fortran, and in other languages that have versions of them. Their beauty has always been that computer manufacturers have been encouraged to implement the BLAS as efficiently as possible. The BLAS began with the simple observation that a number of vector operations (dot product, Euclidean norm, vector scale, and add) were commonly implemented in numerical software, and thus a set of Fortran subroutines for them with standardized names was proposed [1]. The linear algebraic equation package (LINPACK) project [2] was built around these routines for the sake of modularity and portability. The vector BLAS are now called level-1 BLAS. Level-2 BLAS (matrix-vector operations) [3], and level-3 BLAS (matrix-matrix operations) [4] were developed in tandem with another linear algebra package (LAPACK) project [5]. Conventional wisdom is that numerical algorithm design should take advantage of level-3 BLAS operations to the greatest extent possible, since this reduces the ratio of (costly) memory references to (cheap) arithmetic operations. This paper updates the ongoing BLAS effort, and summarizes what types of operations are now available. We now have flavors of BLAS for dense, banded, and sparse vector and matrix operations. Some BLAS are also supported in extended and mixed precision. That effort is carefully chronicled here, by some of the many contributors to the BLAS. Online Computing Reviews Service

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 28, Issue 2

June 2002

151 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/567806

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Association for Computing Machinery

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Published: 01 June 2002

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https://dl.acm.org/doi/10.1145/3711871
Leißa RUllrich MMeyer JHack S(2025)MimIR: An Extensible and Type-Safe Intermediate Representation for the DSL AgeProceedings of the ACM on Programming Languages10.1145/37048409:POPL(95-125)Online publication date: 9-Jan-2025
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The BLAS API of BLASFEO: Optimizing Performance for Small Matrices

Efficient model order reduction of large-scale systems on multi-core platforms

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