Speaker
Description
Given two matrices $X,Y\in\mathbb{R}^{n\times m}$ with $m In this talk, we present a randomized version of the algorithm, which computes two matrices Q and P that satisfy the sketched biorthognality condition $(\Omega Q)^T \Omega P = D$, where $\Omega \in\mathbb{R}^{s\times n}$ is a sketching matrix satisfying an oblivious $\varepsilon$-embedding property, such as a subsampled randomized Hadamard transform or a sparse sign matrix. We show how this approach can improve the stability of the algorithm and the condition number of the computed bases $Q$ and $P$. As an application, we consider the computation of approximate eigenvalues and both right and left eigenvectors, where our randomized two-sided Gram-Schmidt orthogonalization process can be implemented within the non-symmetric Lanczos algorithm.
