Quantum mechanics

Algorithm

Gaussian

World Wide Web

Pure mathematics

Division algebra

Materials science

Implementation

Computer graphics (images)

Sparse matrix

Eigenvalues and eigenvectors

Computer science

Polynomial

Slicing

Matrix (chemical analysis)

Software

Physics

Krylov subspace

Mathematical software

Mathematics

Multilinear algebra

Linear algebra

Mathematical analysis

Artificial intelligence

Geometry

Composite material

Programming language

Subspace topology

Filtered algebra

Iterative method

Algebra over a field

SIAM Journal on Scientific Computing

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 name indicates, the package exploits spectrum slicing, a strategy that consists of dividing the spectrum into a number of subintervals and extracting eigenpairs from each subinterval independently. In order to enable such a strategy, the methods in EVSL utilize a quick calculation of the spectral density of a given matrix (or matrix pair). What distinguishes EVSL from other available packages is that EVSL relies entirely on filtering techniques. Both polynomial and rational classes of filtering are implemented and are coupled with Krylov subspace methods as well as subspace iteration. On the implementations, the package offers interfaces for various scenarios including matrix-free approaches, whereby user-specific functions can be supplied to perform matrix-vector operations or solve linear systems. The paper describes the algorithms in EVSL, provides details on their implementations, and discusses performance issues for the various methods and on various computing platforms.

The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software