Fast and accurate randomized algorithms for linear systems and eigenvalue problems - Nakatsukasa, Y; Tropp, JA (Society for Industrial and Applied Mathematics, 2024)
This paper develops a class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized dimension reduction (``sketching"") to accelerate standard subspace projection methods, such as GMRES and Rayleigh--Ritz. This modification makes it possible to incorporate nontraditional bases for the approximation subspace that are easier to construct. When the basis is numerically full rank, the new algorithms have accuracy similar to classic methods but run faster and may use less storage. For model problems, numerical experiments show large advantages over the optimized MATLAB routines, including a 70× speedup over gmres and a 10× speedup over eigs.