10 citations · 45 across the 28 of their papers we have counts for
18 papers · 1 filter
Reducing operator complexity in Algebraic Multigrid with Machine Learning Approaches
Ru Huang, Kai Chang, Huan He +2
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of…
NLTGCR: A class of Nonlinear Acceleration Procedures based on Conjugate Residuals
Huan He, Ziyuan Tang, Shifan Zhao +2
This paper develops a new class of nonlinear acceleration algorithms based on extending conjugate residual-type procedures from linear to nonlinear equations. The main algorithm ha…
An Adaptive Factorized Nyström Preconditioner for Regularized Kernel Matrices
Shifan Zhao, Tianshi Xu, Hua Huang +2
The spectrum of a kernel matrix significantly depends on the parameter values of the kernel function used to define the kernel matrix. This makes it challenging to design a precond…
Data-Driven Linear Complexity Low-Rank Approximation of General Kernel Matrices: A Geometric Approach
Difeng Cai, Edmond Chow, Yuanzhe Xi
A general, {\em rectangular} kernel matrix may be defined as where is a kernel function and where and are two…
Data-driven Construction of Hierarchical Matrices with Nested Bases
Difeng Cai, Hua Huang, Edmond Chow +1
Hierarchical matrices provide a powerful representation for significantly reducing the computational complexity associated with dense kernel matrices. For general kernel functions,…
Fast randomized non-Hermitian eigensolver based on rational filtering and matrix partitioning
Vassilis Kalantzis, Yuanzhe Xi, Lior Horesh
This paper describes a set of rational filtering algorithms to compute a few eigenvalues (and associated eigenvectors) of non-Hermitian matrix pencils. Our interest lies in computi…
Learning optimal multigrid smoothers via neural networks
Ru Huang, Ruipeng Li, Yuanzhe Xi
Multigrid methods are one of the most efficient techniques for solving linear systems arising from Partial Differential Equations (PDEs) and graph Laplacians from machine learning…
Fast deterministic approximation of symmetric indefinite kernel matrices with high dimensional datasets
Difeng Cai, James Nagy, Yuanzhe Xi
Kernel methods are used frequently in various applications of machine learning. For large-scale high dimensional applications, the success of kernel methods hinges on the ability t…
A power Schur complement Low-Rank correction preconditioner for general sparse linear systems
Qingqing Zheng, Yuanzhe Xi, Yousef Saad
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank…
Structured FISTA for Image Restoration
Zixuan Chen, James Nagy, Yuanzhe Xi +1
In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the co…
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…
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…
Beyond AMLS: Domain decomposition with rational filtering
Vassilis Kalantzis, Yuanzhe Xi, Yousef Saad
This paper proposes a rational filtering domain decomposition technique for the solution of large and sparse symmetric generalized eigenvalue problems. The proposed technique is pu…
A Multi-level Mixed Element scheme of the two dimensional helmholtz transmission eigenvalue problem
Y. Xi, X. Ji, S. Zhang
In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by r…
Fast computation of spectral densities for generalized eigenvalue problems
Yuanzhe Xi, Ruipeng Li, Yousef Saad
The distribution of the eigenvalues of a Hermitian matrix (or of a Hermitian matrix pencil) reveals important features of the underlying problem, whether a Hamiltonian system in ph…
SMASH: Structured matrix approximation by separation and hierarchy
Difeng Cai, Edmond Chow, Yousef Saad +1
This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel f…
A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
Ruipeng Li, Yuanzhe Xi, Eugene Vecharynski +2
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywh…
Schur Complement based domain decomposition preconditioners with Low-rank corrections
Ruipeng Li, Yuanzhe Xi, Yousef Saad
This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD)…