GPU acceleration of the semisparse active-column route

Determine whether a GPU implementation of the semisparse active-column Cholesky route can outperform CPU execution, despite small dense BLAS-3 calls, irregular scatter traffic, and heterogeneous tile occupancy.

Background

The paper evaluates a CUDA implementation only for its dense Cholesky route, whose relatively large dense tiles map naturally to cuBLAS and cuSOLVER kernels. It explicitly excludes GPU treatment of the semisparse active-column route because the packed sub-block operations may be too small to offset kernel-launch costs, while the subsequent scatter operations impose irregular memory traffic.

A GPU implementation would also need to mix dense and sparse tile kernels within one schedule and decide per tile which representation is beneficial. The authors therefore leave unresolved whether the semisparse route’s CPU advantages extend to GPU hardware or whether the associated launch and irregular-memory overheads eliminate those benefits.