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A widely used computationally intensive scientific kernel, the matrix multiplication algorithm is at the heart of many scientific routines. Resurging fields, such as artificial intelligence (AI), strongly benefit from fast and accurate processing of large matrices. Through the years, multiple efforts have been made to derive new algorithms capable of achieving better performance than the naive matrix multiplication approach \(\Theta (n^{3})\) . One of those is Strassen’s variant \(\Theta (n^{2.81})\) . This research compares the benefits and differences of using an optimal version of Strassen’s algorithm versus the naive algorithm. The performance analysis makes use of the two most dominant high-performance computing (HPC) architectures available within the Lonestar6 cluster at Texas Advance Computing Center (TACC), the multi-core (CPU) and many-core (GPU) architectures.

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A Comparative Study of Two Matrix Multiplication Algorithms Under Current Hardware Architectures

  • 会议论文

  • 发表日期：

    2025年

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  • Samuel Olatunde,
  • Eduardo Colmenares

摘要

A widely used computationally intensive scientific kernel, the matrix multiplication algorithm is at the heart of many scientific routines. Resurging fields, such as artificial intelligence (AI), strongly benefit from fast and accurate processing of large matrices. Through the years, multiple efforts have been made to derive new algorithms capable of achieving better performance than the naive matrix multiplication approach \(\Theta (n^{3})\) . One of those is Strassen’s variant \(\Theta (n^{2.81})\) . This research compares the benefits and differences of using an optimal version of Strassen’s algorithm versus the naive algorithm. The performance analysis makes use of the two most dominant high-performance computing (HPC) architectures available within the Lonestar6 cluster at Texas Advance Computing Center (TACC), the multi-core (CPU) and many-core (GPU) architectures.