Speaker
Description
Stochastic Lanczos Quadrature (SLQ) is a popular algorithm for approximating the spectral density of a symmetric matrix $A$ using matrix-vector products. We present a variance reduced implementation of SLQ. This implementation has two key ingredients: a faster problem-specific eigensolver and a carefully implemented selective orthogonalization scheme that we use as a deflation criterion. Our eigensolver is observed to be faster, more robust, and to scale better than LAPACK's 'stemr' (MRRR) in the context of SLQ. Equipped with this faster eigensolver, we explicitly track residual information and perform deflation to speed up convergence. This is achieved using an implementation that closely follows the LanSO algorithm described in Parlett's $\textit{The Symmetric Eigenvalue Problem}$.