4 papers · 1 filter
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…
Nearly Optimal Approximation of Matrix Functions by the Lanczos Method
Noah Amsel, Tyler Chen, Anne Greenbaum +2
Approximating the action of a matrix function on a vector is an increasingly important primitive in machine learning, data science, and statistics, wit…
The Lanczos algorithm for matrix functions: a handbook for scientists
Tyler Chen
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulti…
A posteriori error bounds for the block-Lanczos method for matrix function approximation
Qichen Xu, Tyler Chen
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments…