Coordinate-wise descent methods for leading eigenvalue problem
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.