BLR-Krylov: A Single-GPU Iterative SpMM Framework with Communication Avoidance and Block Low-Rank Optimization

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Abstract
Sparse General Matrix Multiplication (SpMM) is a fundamental kernel in iterative scientific computing and graph neural network inference. On single-GPU platforms, iterative SpMM suffers from two major performance bottlenecks: excessive memory traffic caused by repeated loading of Krylov basis vectors, and low computational efficiency due to irregular sparsity patterns. To address these challenges, this article proposes BLR-Krylov , an iterative SpMM optimization framework that integrates Communication-Avoiding Krylov (CA-Krylov) methods with a Block Low-Rank Sparse (BLR-Sparse) matrix format. BLR-Krylov first preprocesses sparse matrices into the BLR-Sparse format, where low-rank blocks are compressed through basis vector decomposition to reduce storage and arithmetic overhead. It then employs GPU-optimized matrix power kernels to batch-compute Krylov subspace basis vectors, effectively minimizing global memory accesses across iterations. Experimental results on multiple GPU architectures demonstrate that BLR-Krylov achieves a 4.0–6.0× speedup over existing communication-avoiding approaches in iterative workloads, increases global memory bandwidth utilization to 82%–87%, and improves tensor core utilization to 85%–92%, while maintaining numerical accuracy within 1 × 10 -6 . To facilitate reproducibility, partial source code is publicly available at https://github.com/19547035579zz-tech/BLR-Krylov.
Funding Information
  • Doctoral Research Foundation of Nanyang Normal University, China (2023ZX008)
  • Joint Fund for Science and Technology Research and Development of Henan province (245101610059)
  • Key Research and Development and Promotion Program of Henan Province, China (242102210184 and 252102210247)
  • National Natural Science Foundation Cultivation Program of China (2025PY036)
  • Science and Technology Program of Nanyang City, China (23JCQY2003)

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