This paper presents the Hager–Zhang (HZ)-type Riemannian conjugate gradient method that uses exponential retraction. We also present global convergence analyses of our proposed under two kinds assumptions. Moreover, we numerically compare methods with existing by solving optimization problems on unit sphere. The numerical results show has much better performance than methods, i.e., FR, DY, PRP,...

In this paper the use of iterative methods for the solution of the carrier continuity equations in three-dimensional semiconductor device simulators is summarized. An overview of the derivation of the linear systems from the basic stationary semiconductor device equations is given and the algebraic properties of the nonsymmetric coefficient matrices are discussed. Results from the following cla...

This paper is concerned with proving theoretical results related to the convergence of the Conjugate Gradient method for solving positive definite symmetric linear systems. New relations for ratios of the A-norm of the error and the norm of the residual are provided starting from some earlier results of Sadok [13]. These results use the well-known correspondence between the Conjugate Gradient m...

In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them is also isomet...