CoordinateWise Descent Methods for Leading Eigenvalue Problem
Yingzhou Li, Jianfeng Lu, Zhe Wang · SIAM Journal on Scientific Computing · 2019
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinatewise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a nonconvex optimization problem. The convergence of several coordinatewise methods is analyzed and compared. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinatewise descent methods.