## A Poly-Algorithm for Parallel Dense Matrix Multiplication on Two-Dimensional Process Grid Topologies (1995)

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### BibTeX

@MISC{Li95apoly-algorithm,

author = {Jin Li and Anthony Skjellum and Robert D. Falgout},

title = {A Poly-Algorithm for Parallel Dense Matrix Multiplication on Two-Dimensional Process Grid Topologies},

year = {1995}

}

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### Abstract

In this paper, we present several new and generalized parallel dense matrix multiplication algorithms of the form C = αAB + βC on two-dimensional process grid topologies. These algorithms can deal with rectangular matrices distributed on rectangular grids. We classify these algorithms coherently into three categories according to the communication primitives used and thus we offer a taxonomy for this family of related algorithms. All these algorithms are represented in the data distribution independent approach and thus do not require a specific data distribution for correctness. The algorithmic compatibility condition result shown here ensures the correctness of the matrix multiplication. We define and extend the data distribution functions and introduce permutation compatibility and algorithmic compatibility. We also discuss a permutation compatible data distribution (modified virtual 2D data distribution). We conclude that no single algorithm always achieves the best performance...