User-side Quality-of-Service (QoS) data are vital for efficient cloud service selection, while available QoS data in real applications are commonly described by a high-dimensional and Sparse (HiDS) matrix due to a) increasing users and services, and b) the impossibility of observing the full invoking mapping among users and services. A latent factor analysis (LFA) model has proven to be efficient in performing representation learning on such an HiDS QoS matrix. However, existing LFA models commonly adopt a first-order optimizer that cannot makes it approach the second-order stationary point of the learning objective, thereby resulting in accuracy loss. Aiming at addressing this issue, this study proposes to incorporate a Generalized Nesterov's Acceleration (GNA) method in to a Hessian-vector algorithm for LFA, thereby establishing a GNA-incorporated Hessian-vector-based LFA (GNHL) model with two-fold ideas: A) adopting the principle of a Hessian-vector method to acquire a proper Newton step efficiently, and b) incorporating a GNA method into its linear search for accelerating its convergence rate. Experimental results on six real QoS datasets demonstrate that a GNHL model outperforms state-of-The-Art LFA models in generating highly accurate predictions for missing QoS data with low computational burden.