A parallel multithreaded sparse triangular linear system solver

A novel graph transformation strategy for optimizing SpTRSV on CPUs

“…Matrix is reordered to help forming blocks around the diagonal and off-diagonal to improve the locality. 9,10,[30][31][32]34 In Reference 9, authors use dense BLAS operations to compute dense off-diagonal blocks. Dense matrix computations have higher parallelism than their sparse counterparts, therefore, creating dense blocks in sparse matrices is an effective method to improve performance.…”

“…It is a method practiced on CPUs more than on GPUs. Matrix is reordered to help forming blocks around the diagonal and off‐diagonal to improve the locality 9,10,30‐32,34 . In Reference 9, authors use dense BLAS operations to compute dense off‐diagonal blocks.…”

“…Different approaches have been taken to attack this problem which are based on partitioning the matrix into smaller pieces and solving them with the appropriate method and/or on the appropriate architecture. “Block‐diagonal based methods” is an umbrella term which is used for such partitioning methods for SpTRSV on CPUs 6 . Partitioning approach is a natural approach for SpTRSV and it has many successful examples in the literature 7‐12 .…”