This paper proposes improvements to the modified Fletcher–Reeves conjugate gradient method (FR-CGM) for computing
-eigenpairs of symmetric tensors. The FR-CGM does not need to compute the exact gradient and Jacobian. The global convergence of this method is established. We also test other conjugate gradient methods such as the modified Polak–Ribière–Polyak conjugate gradient method (PRP-CGM) and shifted power method (SS-HOPM). Numerical experiments of FR-CGM, PRP-CGM and SS-HOPM show the efficiency of the proposed method for finding
-eigenpairs of symmetric tensors.