Linear Algebra Problems Solved by Using Damped Dynamical Systems on the Stiefel Manifold

2025/10/12 by Gulliksson, M, Oleynik, A, Ogren, M +1
#Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2510.10535

Abstract

We develop a new method for solving minimization problems on the Stiefel Manifold using damped dynamical systems. The constraints are satisfied in the limit by an additional damped dynamical system. The method is illustrated by numerical experiments and compared to a state-of-the-art conjugate gradient method.

Citations

• Stochastic asymptotical regularization for nonlinear ill-posed problems
• On the second order asymptotical regularization of linear ill-posed inverse problems
• The Geometry of Algorithms with Orthogonality Constraints

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