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FLAME: Formal Linear Algebra Methods Environment
TLDR
This paper illustrates the observations by looking at the Formal Linear Algebra Methods Environment (FLAME), a framework that facilitates the derivation and implementation of linear algebra algorithms on sequential architectures, and demonstrates that lessons learned in the distributed-memory world can guide us toward better approaches even in the sequential world.
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Automated Empirical Optimization
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The science of deriving dense linear algebra algorithms
TLDR
The method has been shown to yield new high- performance algorithms for well-studied linear algebra operations and should also be of interest to those who wish to produce best-in-class high-performance codes.
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Anatomy of High-Performance Many-Threaded Matrix Multiplication
TLDR
This work describes how BLIS extends the "GotoBLAS approach" to implementing matrix multiplication (GEMM), and shows that with the advent of many-core architectures such as the IBM PowerPC A2 processor and the Intel Xeon Phi processor, parallelizing both within and around the inner kernel, as the BLIS approach supports, is not only convenient, but also necessary for scalability.
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A Family of High-Performance Matrix Multiplication Algorithms
TLDR
Using a simple model of hierarchical memories, mathematics is employed to determine a locally-optimal strategy for blocking matrices and the resulting family of algorithms yields performance that is superior to that of methods that automatically tune such kernels.
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PLAPACK: Parallel Linear Algebra Package
TLDR
The PLAPACK project represents an eeort to provide an infrastructure for implementing application friendly high performance linear algebra algorithms by using a more application-centric data distribution, as well as an object based (MPI-like) style of programming.
PLAPACK: high performance through high-level abstraction
TLDR
This paper shows that by coding at a higher level of abstraction, more sophisticated algorithms can be implemented, which allows high levels of performance to be regained for the parallel solver package implemented using PLAPACK.
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On Global Combine Operations
  • R. Geijn
  • Mathematics
    J. Parallel Distributed Comput.
  • 1 August 1994
TLDR
A hybrid strategy for implementing global combine operations on distributed memory Multiple Instruction Multiple Data multicomputers and results from its implementation on the Intel iPSC/860 are reported.
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Parallel Matrix Multiplication: A Systematic Journey
TLDR
The paper introduces a taxonomy for the resulting family of algorithms and explains how all algorithms have merit depending on parameters such as the sizes of the matrices and architecture parameters.
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Parallel implementation of BLAS: general techniques for Level 3 BLAS
TLDR
It is shown that the techniques used for the matrix-matrix multiplication naturally extend to all important level 3 BLAS and thus this approach becomes an enabling technology for efficient parallel implementation of these routines and libraries that use BLAS.
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