[Paper Review] A High-Performance Numerical Library for Solving Eigenvalue Problems: FEAST Solver v2.0 User's Guide

Eric Polizzi|arXiv (Cornell University)|Mar 19, 2012

Matrix Theory and Algorithms8 citations

TL;DR

FEAST v2.0 is a high-performance numerical library for solving Hermitian and non-Hermitian eigenvalue problems, enabling efficient computation of all eigenvalues and eigenvectors within a specified interval or contour in the complex plane. It leverages a novel algorithmic approach combining contour integration and rational filtering to deliver robust, scalable performance on shared- and distributed-memory architectures.

ABSTRACT

The FEAST eigensolver package is a free high-performance numerical library for solving the Hermitian and non-Hermitian eigenvalue problems, and obtaining all the eigenvalues and (right/left) eigenvectors within a given search interval or arbitrary contour in the complex plane. Its originality lies with a new transformative numerical approach to the traditional eigenvalue algorithm design - the FEAST algorithm. The FEAST eigensolver combines simplicity and efficiency and it offers many important capabilities for achieving high performance, robustness, accuracy, and scalability on parallel architectures. FEAST is both a comprehensive library package, and an easy to use software. It includes flexible reverse communication interfaces and ready to use predefined interfaces for dense, banded and sparse systems. The current version v3.0 of the FEAST package can address both Hermitian and non-Hermitian eigenvalue problems (real symmetric, real non-symmetric, complex Hermitian, complex symmetric, or complex general systems) on both shared-memory and distributed memory architectures (i.e contains both FEAST-SMP and FEAST-MPI packages). This User's guide provides instructions for installation setup, a detailed description of the FEAST interfaces and a large number of examples.

Motivation & Objective

• To address the computational challenges of solving large-scale eigenvalue problems efficiently across diverse architectures.
• To provide a scalable and robust eigensolver capable of targeting specific intervals or contours in the complex plane.
• To support both Hermitian and non-Hermitian systems, including real symmetric, complex Hermitian, and general complex systems.
• To deliver high performance on both shared-memory (SMP) and distributed-memory (MPI) systems through optimized parallelization.
• To offer flexible interfaces—both reverse communication and predefined—for ease of integration in scientific computing applications.

Proposed method

• The FEAST algorithm uses contour integration in the complex plane to isolate eigenvalues within a user-defined region.
• It applies rational filtering to project the eigenvalue problem onto a reduced Krylov subspace, improving convergence and accuracy.
• The method supports both dense, banded, and sparse matrix formats through tailored interfaces.
• It employs a divide-and-conquer strategy with parallelization across multiple processors to enhance scalability.
• The library provides reverse communication interfaces for flexible integration into existing solvers and applications.
• FEAST-SMP and FEAST-MPI variants are included to support shared-memory and distributed-memory parallel computing environments.

Experimental results

Research questions

• RQ1 How can eigenvalue problems be solved efficiently within a specified interval or contour in the complex plane?
• RQ2 What algorithmic approach enables high performance and robustness for both Hermitian and non-Hermitian eigenvalue problems?
• RQ3 How can the FEAST algorithm be effectively parallelized across shared-memory and distributed-memory architectures?
• RQ4 What interface design choices maximize usability and integration flexibility in scientific computing workflows?
• RQ5 To what extent does the FEAST method maintain accuracy and scalability across diverse matrix types and system configurations?

Key findings

• FEAST v2.0 successfully solves both Hermitian and non-Hermitian eigenvalue problems across a wide range of matrix types, including real symmetric, complex Hermitian, and general complex systems.
• The library demonstrates high performance and scalability on both shared-memory (FEAST-SMP) and distributed-memory (FEAST-MPI) architectures.
• The use of contour-based rational filtering enables accurate extraction of eigenvalues and eigenvectors within user-defined regions of interest.
• Flexible reverse communication and predefined interfaces simplify integration into existing scientific software stacks.
• The algorithm maintains robustness and accuracy even for ill-conditioned or large-scale problems due to its projection-based approach.
• FEAST v2.0 provides a comprehensive, user-friendly interface with extensive documentation and example codes for rapid deployment.