274 citations · 661 across the 37 of their papers we have counts for
5 papers · 2 filters
Solving the 3D High-Frequency Helmholtz Equation using Contour Integration and Polynomial Preconditioning
Xiao Liu, Yuanzhe Xi, Yousef Saad +1
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the sol…
Find the dimension that counts: Fast dimension estimation and Krylov PCA
Shashanka Ubaru, Abd-Krim Seghouane, Yousef Saad
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating t…
Spectrum-Adapted Polynomial Approximation for Matrix Functions
Li Fan, David I Shuman, Shashanka Ubaru +1
We propose and investigate two new methods to approximate for large, sparse, Hermitian matrices . The main idea behind both methods is to first estimat…
The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
Ruipeng Li, Yuanzhe Xi, Lucas Erlandson +1
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its n…
A Posteriori Error Estimate for Computing by Using the Lanczos Method
Jie Chen, Yousef Saad
An outstanding problem when computing a function of a matrix, , by using a Krylov method is to accurately estimate errors when convergence is slow. Apart from the case of the…