4 papers
An analysis on stochastic Lanczos quadrature with asymmetric quadrature nodes
Wenhao Li, Yixuan Huang, Shengxin Zhu
This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczo…
On Symmetric Lanczos Quadrature for Stochastic Trace Estimation
Wenhao Li, Shengxin Zhu
A common approach to approximating quadratic forms of matrix functions is to use a quadrature rule derived from the Lanczos process, known as a Lanczos quadrature. Although symmetr…
When Lanczos Iterations Generate Symmetric Quadrature Nodes?
Wenhao Li, Zongyuan Han, Shengxin Zhu
The Golub-Welsch algorithm [ Math. Comp., 23: 221-230 (1969)] has long been assumed symmetric for estimating quadratic forms. Recent research indicates that asymmetric quadrature n…
Stochastic diagonal estimation with adaptive parameter selection
Zongyuan Han, Wenhao Li, Shengxin Zhu
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter…