Alternating least squares (ALS) is a powerful matrix factor- ization (MF) algorithm for both explicit and implicit feed- back based recommender systems. As shown in many articles, increasing the number of latent factors (denoted by K) boosts the prediction accuracy of MF based recommender systems, including ALS as well. The price of the better accuracy is paid by the increased running time: the running time of the original version of ALS is proportional to K 3. Yet, the running time of model building can be important in recommendation systems; if the model cannot keep up with the changing item portfolio and/or user profile, the predic- tion accuracy can be degraded. In this paper we present novel and fast ALS variants both for the implicit and explicit feedback datasets, which offers better trade-off between running time and accuracy. Due to the significantly lower computational complexity of the algorithm-linear in terms of K-the model being generated under the same amount of time is more accurate, since the faster training enables to build model with more latent factors. We demonstrate the efficiency of our ALS variants on two datasets using two performance measures, RMSE and average relative position (ARP), and show that either a significantly more accurate model can be generated under the same amount of time or a model with similar predic- tion accuracy can be created faster; for explicit feedback the speed-up factor can be even 5-10.