Spectral residual method for nonlinear equations on Riemannian manifolds

In this paper, the spectral algorithm for nonlinear equations (SANE) is adapted to problem of finding a zero given tangent vector field on Riemannian manifold. The generalized version SANE uses, in systematic way, as search direction and continuous real-valued function that adapts ensures it verifies descent condition an associated merit function. To speed up convergence proposed method, we incorporate adaptive parameter combination with non-monotone globalization technique. global procedure established under some standard assumptions. Numerical results indicate our very effective efficient solving different manifolds competes favorably Polak–Ribiére–Polyak method recently published other methods existing literature.