LINPACK

LINPACK is a software package and benchmark used to measure the floating-point performance of computers by solving dense systems of linear equations. It originated in the 1970s as part of work by Jack Dongarra and colleagues to provide a portable benchmark for numerical linear algebra on various architectures.

At its core, the classic LINPACK benchmark solves a system A x = b by Gaussian elimination with partial pivoting. For an n-by-n matrix, the LU factorization with pivoting requires about (2/3) n^3 floating-point operations; the run time is recorded and reported as the achieved performance in FLOPS, commonly expressed in gigaflops (GFLOPS) for large n. Most runs use double precision arithmetic and rely on optimized BLAS routines.

High-Performance LINPACK (HPL) extends the idea to distributed-memory systems, solving the same type of problem with very large matrices using LU decomposition with partial pivoting and Level-3 BLAS. HPL is the benchmark that underpins the Top500 list, which ranks supercomputers by their Rmax—the highest measured LINPACK performance, usually reported in GFLOPS.

LINPACK has played a significant role in the development of high-performance computing by providing a standardized metric. However, it primarily measures peak performance for dense linear algebra and can misrepresent other workloads; memory bandwidth, communication costs, and software efficiency substantially influence results. Consequently, practitioners supplement LINPACK with other benchmarks to gain a broader view of system performance.