Explanipedia

Mixed Precision Iterative Refinement for Least Squares With Linear Equality Constraints and Generalized Least Squares Problems Open

Bowen Gao, Yuxin Ma, Meiyue Shao · 2025

Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which is the solver for the least squares problem. By transforming least squares problems into augmented linear…

A Mixed Precision Jacobi SVD Algorithm Open

Wen-Jing Gao, Yuxin Ma, Meiyue Shao · 2025

We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and t…

On a shrink-and-expand technique for symmetric block eigensolvers Open

Yuqi Liu, Ma Yuxin, Meiyue Shao · 2024

In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid con…

Mixed precision iterative refinement for least squares with linear equality constraints and generalized least squares problems Open

Bowen Gao, Yuxin Ma, Meiyue Shao · 2024

Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least squ…

A fast low-rank inversion algorithm of dielectric matrix in GW approximation Open

Zhengbang Zhou, Huanhuan Ma, Wentiao Wu, Weiguo Gao, Jinlong Yang , et al. · 2024

The dielectric response function and its inverse are crucial physical quantities in materials science. We propose an accurate and efficient strategy to invert the dielectric function matrix. The GW approximation, a powerful approach to acc…

A Contour Integral-Based Algorithm for Computing Generalized Singular Values Open

Yuqi Liu, Xinyu Shan, Meiyue Shao · 2023

We propose a contour integral-based algorithm for computing a few singular values of a matrix or a few generalized singular values of a matrix pencil. Mathematically, the generalized singular values of a matrix pencil are the eigenvalues o…

A mixed precision LOBPCG algorithm Open

Daniel Kreßner, Yuxin Ma, Meiyue Shao · 2023

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positivedefinite matrix A . In this work,…

A mixed precision LOBPCG algorithm Open

Daniel Kreßner, Yuxin Ma, Meiyue Shao · 2023

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work,…

A mixed precision Jacobi SVD algorithm Open

Weiguo Gao, Yuxin Ma, Meiyue Shao · 2022

We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess, and …

Householder orthogonalization with a non-standard inner product Open

Meiyue Shao · 2021

Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning of the input. However, in the context of a non-standard inner product, it becomes difficult …

Ab Initio No Core Shell Model with Leadership-Class Supercomputers Open

James P. Vary, Hasan Metin Aktulga, Meiyue Shao, Weijie Du, Dossay Oryspayev , et al. · 2018

Nuclear structure and reaction theory is undergoing a major renaissance with advances in many-body methods, strong interactions with greatly improved links to Quantum Chromodynamics (QCD), the advent of high performance computing, and impr…

Accelerating Optical Absorption Spectra and Exciton Energy Computation for Nanosystems via Interpolative Separable Density Fitting Open

Wei Hu, Meiyue Shao, Andrea Cepellotti, Felipe H. da Jornada, Lin Lin , et al. · 2018

We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the…

A Robust and Efficient Implementation of LOBPCG Open

Jed A. Duersch, Meiyue Shao, Chao Yang, Ming Gu · 2018

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely\nused to compute eigenvalues of large sparse symmetric matrices. The algorithm\ncan suffer from numerical instability if it is not implemented with care. This\nis e…

Accelerating Optical Absorption Spectra and Exciton Energy Computation via Interpolative Separable Density Fitting Open

Wei Hu, Meiyue Shao, Andrea Cepellotti, Felipe H. da Jornada, Lin Lin , et al. · 2018

A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum Open

Meiyue Shao, Felipe H. da Jornada, Lin Lin, Chao Yang, Jack Deslippe , et al. · 2018

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure …

Properties of Definite Bethe–Salpeter Eigenvalue Problems Open

Meiyue Shao, Chao Yang · 2017

BSEPACK User's Guide Open

Meiyue Shao, Chao Yang · 2016

This is the user manual for the software package BSEPACK (Bethe--Salpeter Eigenvalue Solver Package).

A structure preserving Lanczos algorithm for computing the optical absorption spectrum Open

Meiyue Shao, Felipe H. da Jornada, Lin Lin, Chao Yang, Jack Deslippe , et al. · 2016

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure …

molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters Open

Fabien Bruneval, Tonatiuh Rangel, Samia M. Hamed, Meiyue Shao, Chao Yang , et al. · 2016

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT Open

Jiří Brabec, Lin Lin, Meiyue Shao, Niranjan Govind, Chao Yang , et al. · 2015

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the produ…

Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem Open

Meiyue Shao, Felipe H. da Jornada, Chao Yang, Jack Deslippe, Steven G. Louie · 2015

Development of the FHR advanced natural circulation analysis (Fancy) code Open

Ziyan Guo, Nicolas Zweibaum, Meiyue Shao, LR Huddar, Per F. Peterson , et al. · 2015

The University of California, Berkeley (UCB) is performing thermal hydraulics safety analysis to develop the technical basis for design and licensing of fluoride-salt-cooled, high-temperature reactors (FHRs). FHR designs investigated by UC…

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