Solving Dense Generalized Eigenproblems on Multi-threaded Architectures

TL;DR

This paper compares reduction to tridiagonal form and Krylov-subspace iteration methods for solving dense symmetric generalized eigenproblems, demonstrating that iterative methods can be competitive on modern multi-core and GPU architectures.

Contribution

It provides a performance comparison of two approaches on real applications, highlighting the effectiveness of Krylov methods for dense problems on advanced hardware.

Findings

Krylov methods are competitive for dense eigenproblems on multi-core and GPU systems.

Performance depends on application, architecture, and parallelism.

Experimental results on large-scale applications validate the approaches.

Abstract

We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale applications, arising in molecular dynamics and material science, are employed to investigate the contributions of the application, architecture, and parallelism of the method to the performance of the solvers. The experimental results on a state-of-the-art 8-core platform, equipped with a graphics processing unit (GPU), reveal that in real applications, iterative Krylov-subspace methods can be a competitive approach also for the solution of dense problems.