Scientists Find Way to Make GPUs Twice as Fast at Key Calculations

Researchers developed HSMA-TRSM, a new optimization framework for Triangular Solve with Multiple Right-hand Sides (TRSM), a fundamental BLAS Level-3 operation that underpins LU/Cholesky decomposition, sparse direct solvers, and matrix inversion. The framework targets left-side lower-triangular TRSM on NVIDIA A100, NVIDIA H800, and Hygon DCU Z100 accelerators. For small-scale cases, it uses a pipelined compute-memory overlap mechanism and a dual thread-group seven-stage pipeline strategy to tackle shared memory limits for double complex types. For large-scale problems, it introduces a diagonal block decoupling optimization with adaptive block size selection. Evaluated on these platforms, HSMA-TRSM achieves peak speedups of 2.05x over cuBLAS and 2.06x over rocBLAS. The work was accepted for the 55th International Conference on Parallel Processing (ICPP '26).