Preconditioning without a preconditioner using block Krylov subspace methods

Tyler Chen presents randomized block conjugate gradient for one positive-definite linear system. The method can provably outperform conjugate gradient with a broad class of Nyström preconditioners while avoiding explicit preconditioner construction. Its analysis also yields guarantees for new Nyström-preconditioned variants. Applications include computing a complete ridge-regression regularization path and drawing multiple independent samples from a high-dimensional Gaussian distribution.