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math.NA2025
The Akhiezer iteration and inverse-free solvers for Sylvester matrix equations
Cade Ballew, Thomas Trogdon, Heather Wilber
Two inverse-free iterative methods are developed for solving Sylvester matrix equations when the spectra of the coefficient matrices are on, or near, known disjoint subintervals of…
math.NA2024
Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanc…
math.NA2024
On the convergence of Fourier spectral methods involving non-compact operators
Thomas Trogdon
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations . The framework posits the existence…