Randomized block Krylov methods for approximating extreme eigenvalues

Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues symmetric matrix or singular values general matrix. The purpose this paper is to develop new theoretical bounds on performance randomized these problems. For matrices with polynomial spectral decay, method can obtain an accurate norm estimate using only constant number steps (that depends decay rate and accuracy). Furthermore, analysis reveals that behavior algorithm in delicate way size. Numerical evidence confirms predictions.