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Acceleration of Approximate Matrix Multiplications on GPUs.

Takuya Okuyama1, André Röhm1, Takatomo Mihana1

  • 1Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

Entropy (Basel, Switzerland)
|August 26, 2023
PubMed
Summary
This summary is machine-generated.

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This study introduces an improved Monte Carlo approximate matrix multiplication (AMM) method for faster scientific calculations. The new approach accelerates eigenvalue computations on GPUs without increasing processing time.

Area of Science:

  • Scientific Computing
  • Numerical Analysis
  • High-Performance Computing

Background:

  • Matrix multiplication is crucial for scientific computing, impacting eigenvalue computation and optimization.
  • Existing methods like GPUs and specialized libraries accelerate matrix products, but accelerating approximate matrix multiplication (AMM) on GPUs remains underexplored.

Purpose of the Study:

  • To develop an enhanced Monte Carlo AMM method optimized for GPU acceleration.
  • To provide an analytical solution for optimal hyperparameter tuning in the proposed AMM method.
  • To demonstrate the method's effectiveness in accelerating eigenvalue computations.

Main Methods:

  • Proposed a novel Monte Carlo AMM algorithm designed for parallel GPU execution.
  • Derived an analytical solution for optimizing hyperparameters within the AMM method.
Keywords:
GPU computingapproximate calculationapproximate matrix multiplication

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  • Integrated the enhanced AMM into the power method for eigenvalue calculation.

    • Main Results:

    • The proposed AMM method enhances approximation accuracy without increasing computation time compared to conventional AMMs.
    • The method is well-suited for GPU parallelization and integration into diverse algorithms.
    • Application to eigenvalue computation on an NVIDIA A100 GPU halved the computation time versus the standard power method using cuBLAS.

    Conclusions:

    • The novel AMM method offers significant speedups for scientific computations on GPUs.
    • This research bridges the gap in accelerating AMMs for general matrices on GPUs.
    • The method shows promise for broader applications in scientific and practical calculations requiring fast matrix products.