Computational forces in the Linpack benchmark

Dimensional analysis reduces a complicated ten-parameter formula for the execution time of the Linpack benchmark to a simpler two-parameter formula. These two parameters are ratios of software forces and hardware forces that determine a self-similarity surface. Machines move along paths on this surface as the problem size and the number of processors change. Two machines scale the same way, they move along the same path, if they have the same hardware forces. To design efficient algorithms, the programmer must produce software forces large enough to overcome the hardware forces. Modern machines have larger hardware forces than older machines and are harder to program.