Computational Materials Science and Engineering

DOI10.1007/978-3-030-43736-7_5zbMath1455.65005OpenAlexW3038659012MaRDI QIDQ3300493

Eric Polizzi, Yousef Saad

Publication date: 29 July 2020

Published in: Parallel Algorithms in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-43736-7_5

zbMATH Keywords

iterative methodsnumerical linear algebrapartial differential equationsdirect methodsnumerical discretizations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Applications to the sciences (65Z05) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Uses Software

• PROPACK
• FEAST
• SIESTA
• IRAM
• MIKA
• CIRR
• SelInv
• PARSEC
• EVSL
• PEXSI

Cites Work

• Self-consistent-field calculations using Chebyshev-filtered subspace iteration
• Analysis of the symmetric Lanczos algorithm with reorthogonalization methods
• A projection method for generalized eigenvalue problems using numerical integration.
• Object-oriented construction of a multigrid electronic-structure code with Fortran 90
• Solution of large eigenvalue problems in electronic structure calculations
• A parallel Lanczos method for symmetric generalized eigenvalue problems
• CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems
• Approximating Spectral Densities of Large Matrices
• A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems
• FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
• Efficient estimation of eigenvalue counts in an interval
• SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
• The Lanczos Algorithm With Partial Reorthogonalization
• Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software
• Electronic Structure
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