Gauss-Seidel is 5x slower than Jacobi — and loop unrolling alone won't fix it

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

Gauss-Seidel converges in half the iterations of Jacobi, yet runs 4–5 times slower because its in-place update creates a loop-carried dependency that blocks vectorization. Using OSACA on compiled assembly, the author measures a 12-cycle latency bound per element versus Jacobi's 1-cycle dependency and 3-cycle throughput floor. Naive unrolling fails because the dependency is mathematical, not a compiler oversight. The post explores how to rewrite the dependency away to recover Gauss-Seidel's convergence advantage without sacrificing hardware efficiency.