The analytical idea
Power iteration estimates the dominant eigenvalue and eigenvector of a matrix—an operation connected to methods such as principal component analysis. The repositories explore NumPy and Numba implementations plus batch execution through Slurm.
Benchmark design
A meaningful performance comparison requires the same workload and numerical conditions. The controlled benchmark gives both implementations the same seeded matrix, starting vector, convergence tolerance, and iteration limit. It warms up compilation, reports median timing, and validates both estimates against NumPy’s symmetric eigensolver.
Companion Monte Carlo experiment
A second repository estimates pi from one million random samples using Numba’s nopython mode. Its recorded Slurm run produced 3.140052, connecting simulation, compiled Python, and batch execution in one compact experiment.
What the work demonstrates
Together, the projects show numerical-method implementation, compiled Python loops, batch-computing exposure, validation against a trusted solver, and disciplined performance measurement. The key limitation is that timing conclusions remain specific to the tested workloads and environment.