Topic: Eigenvalues and spectra

David Woodruff develops sampling bounds for estimating the spectrum of symmetric matrices with bounded entries. Principal-submatrix sampling achieves epsilon times n additive error using roughly 1/epsilon² samples, eliminating dependence on n and improving prior epsilon dependence up to logarithmic factors. Squared row-norm sampling gives epsilon times the Frobenius norm accuracy with roughly 1/epsilon² samples, improving a previous 1/epsilon⁸ bound. For bounded-entry positive-semidefinite matrices, O(1/epsilon) sampled columns permit nonadaptive approximation of the leading eigenvector with e

Daniel Kressner surveys randomized algorithms for joint eigenvalue problems: finding common eigenvectors and their eigenvalues across a family of matrices. The talk covers algorithm development and analysis, with examples from signal processing and multivariate root finding. Joint work with Haoze He and Bor Plestenjak.