Coordinate-wise descent methods for leading eigenvalue problem

TL;DR

This paper explores coordinate-wise descent algorithms for large-scale leading eigenvalue problems, reformulating them as non-convex optimization tasks, analyzing convergence, and demonstrating their effectiveness through quantum physics applications.

Contribution

It introduces and analyzes coordinate-wise descent methods for large eigenvalue problems, providing convergence results and practical benchmarks.

Findings

Methods converge under certain conditions

Numerical examples show high efficiency

Benchmarks compare favorably with existing approaches

Abstract

Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex optimization problem. The convergence of several coordinate-wise methods is analyzed and compared. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinate-wise descent methods.