Gustafson's law models speedup when problem size grows with hardware (weak scaling), yielding near-linear speedup: $S(n) = n - \alpha(n-1)$ where $\alpha$ is the sequential fraction. Unlike Amdahl's law, speedup grows with processor count, making it applicable to most HPC workloads that scale problem size with available hardware.
At 1% sequential overhead and 256 cores, expected speedup is ~250×. This reflects real practice: larger machines solve larger problems, not the same problem faster.
This table shows speedup scaling with problem size (Gustafson regime).
Sequential fraction (α) S(n=16) S(n=64) S(n=256) 1% ≈15.8× ≈63.4× ≈253.5× 5% ≈15.2× ≈60.8× ≈243.2× 10% ≈14.5× ≈58.5× ≈230.4×