4 papers · 1 filter
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…
Suboptimal subspace construction for log-determinant approximation
Zongyuan Han, Wenhao Li, Yixuan Huang +1
Variance reduction is a crucial idea for Monte Carlo simulation and the stochastic Lanczos quadrature method is a dedicated method to approximate the trace of a matrix function. In…
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…