Eigenvalue Problems

Solving dense eigenvalue problems (Ax = λx) for symmetric or Hermitian matrices is a cornerstone of many scientific and engineering disciplines, including quantum chemistry (e.g., electronic structure calculations), condensed matter physics, structural mechanics, and principal component analysis in data science. These problems typically involve finding all or a subset of eigenvalues and eigenvectors of large, dense matrices. The computational cost often scales as O(N^3) with matrix size N, and memory requirements can be substantial, making efficient parallel algorithms and high-performance libraries essential for tackling large-scale simulations on modern HPC systems.

To be updated

Many scientific applications require only a fraction of the eigenvalue spectrum (e.g., eigenvalues near a certain energy or the k smallest/largest). Selected eigenvalue solvers are optimized for this task, often outperforming full spectrum solvers significantly. This benchmark evaluates the time to compute a fixed percentage (e.g., 10%) of eigenpairs for large matrices, as well as the achieved accuracy.

To be updated

Evaluating the parallel scaling efficiency of eigenvalue solvers is crucial for their effective use on large HPC clusters. This benchmark assesses both strong scaling (fixed total problem size, increasing compute nodes) and weak scaling (fixed problem size per node, increasing compute nodes) for leading libraries.

To be updated

Memory footprint can be a critical limiting factor for large-scale eigenvalue calculations. This benchmark compares the peak memory usage (per node or total) of different eigenvalue solvers for a standardized large problem (e.g., 100K x 100K matrix), highlighting libraries with more memory-frugal algorithms or implementations.

To be updated