Collaborative filtering algorithms are important building blocks in many practical recommendation systems. For example, many large-scale data processing environments include collaborative filtering models for which the Alternating Least Squares (ALS) algorithm is used to compute latent factor matrix decompositions. In this paper, we propose an approach to accelerate the convergence of parallel ALS-based optimization methods for collaborative filtering using a nonlinear conjugate gradient (NCG) wrapper around the ALS iterations. We also provide a parallel implementation of the accelerated ALS-NCG algorithm in the Apache Spark distributed data processing environment, and an efficient line search technique as part of the ALS-NCG implementation that requires only one pass over the data on distributed datasets. In serial numerical experiments on a linux workstation and parallel numerical experiments on a 16 node cluster with 256 computing cores, we demonstrate that the combined ALS-NCG method requires many fewer iterations and less time than standalone ALS to reach movie rankings with high accuracy on the MovieLens 20M dataset. In parallel, ALS-NCG can achieve an acceleration factor of 4 or greater in clock time when an accurate solution is desired; furthermore, the acceleration factor increases as greater numerical precision is required in the solution. In addition, the NCG acceleration mechanism is efficient in parallel and scales linearly with problem size on synthetic datasets with up to nearly 1 billion ratings. The acceleration mechanism is general and may also be applicable to other optimization methods for collaborative filtering.