Riemannian Gradient Algorithm for the Numerical Solution of Stein Equations

A Riemannian gradient algorithm based on information geometric structures of a manifold consisting of all symmetric positive-definite matrices was proposed to calculate the numerical solution of Stein equations. In this algorithm, the geodesic distance on the curved Riemannian manifoldis taken as an objective function and the geodesic curve was treated as the convergence path. Also the optimal variable step-sizes corresponding to the minimum value of the objective function were provided in order to improve the convergence speed.