Multicast beamforming is a part of the Evolved Multimedia Broadcast Multicast Service (eMBMS) in the Long-Term Evolution (LTE) standard for efficient audio and video streaming. The associated beamformer design problem has drawn considerable attention over the last decade, but existing solutions are not quite satisfactory. The core problem is NP-hard, and the available approximations leave much to be desired in terms of achieving favorable performance-complexity trade-offs, especially for online implementation. This paper introduces a new class of adaptive multicast beamforming algorithms that simultaneously cover all bases - featuring guaranteed convergence and state-of-art performance at low complexity. Each update takes a step in the direction of an inverse Signal to Noise Ratio (SNR) weighted linear combination of the SNR-gradient vectors of all users. Convergence is established by recourse to proportional fairness. Simulation results show that the proposed algorithms outperform Semi-Definite Relaxation (SDR) and Successive Linear Approximation (SLA - the prior state-of-art) at an order of magnitude lower complexity.