Sparse triangular solves (SpTRSV) form the latency–critical inner loop of many direct and iterative solvers, but strong data dependencies limit thread–level parallelism and make the kernel dominated by memory–latency.
This thesis explores whether redundant computation can be exchanged for improved data locality to accelerate SpTRSV on cache-based multi-core CPUs.

The proposed two-phase algorithm first uses the Recursive Algebraic Colouring Engine (RACE) to permute an arbitrary sparse triangular factor into a block-lower–bidiagonal form whose diagonal blocks fit into a private L2 cache.
Each block is then solved twice: an independent provisional pass followed by a lightweight correction that re-uses the still-resident data.
The resulting task graph halves the critical path, exposes ample parallelism, and leaves total memory traffic unchanged.

An OpenMP5.0 implementation employs the new affinity clause so that producer–consumer task pairs are likely to run on the same core.
Performance is compared against IntelMKL’s sparse triangular routine and the Kokkos-Kernels sptrsv, while LIKWID counters validate cache behaviour.

On a 24-core Cascade Lake node of the DelftBlue supercomputer the task graph achieves a strong-scaling speed-up between 1.25 and 1.45 that saturates after roughly six threads; Kokkos attains similar absolute time only beyond sixteen threads.
With 24 threads the solver is up to an order of magnitude faster than single-threaded MKL, and the affinity hint alone accelerates execution by 1.1–2 times, confirming the importance of cache reuse.
MKL remains preferable for small or highly structured SPD matrices, but on irregular, memory-bound factors the new solver rivals state-of-the-art libraries despite its simple prototype status.