ChASE: Chebyshev Accelerated Subspace iteration Eigensolver for sequences of Hermitian eigenvalue problems

TL;DR

ChASE is a C++ library that efficiently solves sequences of Hermitian eigenproblems by exploiting spectral correlations, outperforming direct solvers especially for extremal spectra, and supports modern parallel architectures.

Contribution

The paper introduces ChASE, a novel polynomial-accelerated subspace iteration eigensolver that leverages spectral properties of eigenproblem sequences for improved efficiency.

Findings

ChASE outperforms direct solvers on many sequences of eigenproblems.

Spectral estimates and polynomial degree optimization reduce FLOPs.

Supports distributed GPU execution and is easily integrable.

Abstract

Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take the form of correlations between the eigenvectors of consecutive problems, as is the case in many real-world applications, the potential benefit of exploiting them can be substantial. We present ChASE, a modern algorithm and library based on subspace iteration with polynomial acceleration. Novel to ChASE is the computation of the spectral estimates that enter in the filter and an optimization of the polynomial degree which further reduces the necessary FLOPs. ChASE is written in C++ using the modern software engineering concepts which favor a simple integration in application codes and a straightforward portability over heterogeneous platforms. When solving sequences of Hermitian eigenproblems for a portion of their extremal spectrum, ChASE greatly benefits from the sequence's spectral properties and outperforms direct solvers in many scenarios. The library ships with two distinct parallelization schemes, supports execution over distributed GPUs, and it is easily extensible to other parallel computing architectures.