2 citations · 3 across the 7 of their papers we have counts for
5 papers · 1 filter
Convergence of pivoted Cholesky for Lipschitz kernels
Sungwoo Jeong, Alex Townsend, Christopher Wang
We investigate the continuous analogue of the Cholesky factorization, namely the pivoted Cholesky algorithm. Our analysis establishes quantitative convergence guarantees for kernel…
Extending Mercer's expansion to indefinite and asymmetric kernels
Sungwoo Jeong, Alex Townsend
Mercer's expansion and Mercer's theorem are cornerstone results in kernel theory. While the classical Mercer's theorem only considers continuous symmetric positive definite kernels…
Operator learning for hyperbolic partial differential equations
Christopher Wang, Alex Townsend
We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from i…
ContHutch++: Stochastic trace estimation for implicit integral operators
Jennifer Zvonek, Andrew Horning, Alex Townsend
Hutchinson's estimator is a randomized algorithm that computes an -approximation to the trace of any positive semidefinite matrix using matrix-vector produc…
Continuous analogues of Krylov methods for differential operators
Marc Aurèle Gilles, Alex Townsend
Analogues of the conjugate gradient method, MINRES, and GMRES are derived for solving boundary value problems (BVPs) involving second-order differential operators. Two challenges a…