  This paper presents new Riemannian conjugate gradient methods and global
convergence analyses under the strong Wolfe conditions. The main idea of the
new methods is to combine the good global convergence properties of the
Dai-Yuan method with the efficient numerical performance of the
Hestenes-Stiefel method. The proposed methods compare well numerically with the
existing methods for the Rayleigh quotient minimization problem on the unit
sphere. Numerical comparisons show that they perform better than the existing
ones.
