Measuring Gauss-Seidel loop-carried dependency and fixing it via loop unrolling

This article shows that a numerically superior algorithm can still deliver worse business performance if its implementation blocks modern CPU optimization: Gauss-Seidel converges in fewer iterations than Jacobi, but loop-carried dependencies prevent vectorization and make it 4–5x slower in wall-clock time. For CIOs and technology leaders, the key implication is that application performance depends as much on hardware-aware coding, compiler behavior, and memory access patterns as it does on the math itself, so IT organizations need stronger performance engineering practices to avoid hidden compute costs. The article also highlights loop unrolling as a practical path to preserve Gauss-Seidel’s convergence advantage while restoring much of the hardware efficiency that enterprise workloads require.