Eigen-decomposition-based direction finding methods of using large-scale/ultra-large-scale fully-digital receive antenna arrays lead to a high or ultra-high complexity. To address the complexity dilemma, in this paper, three low-complexity estimators are proposed: partitioned subarray auto-correlation combining (PSAC), partitioned subarray cross-correlation combining (PSCC) and power iteration max correlation successive convex approximation (PI-Max-CSCA). Compared with the conventional no-partitioned direction finding method like root multiple signal classification (Root-MUSIC), in the PSAC method, the total set of antennas are equally partitioned into subsets of antennas, called subarrays, each subarray performs independent DOA estimation, and all DOA estimates are coherently combined to give the final estimation. For a better performance, the cross-correlation among sub-arrays is further exploited in the PSCC method to achieve the near-Cramer-Rao lower bound (CRLB) performance with the help of auto-correlation. To further reduce the complexity, in the PI-Max-CSCA method, using a fraction of all subarrays to make an initial coarse direction measurement (ICDM), the power iterative method is adopted to compute the more precise steering vector (SV) by exploiting the total array, and a more accurate DOA value is found using ICDM and SV through the maximum correlation method solved by successive convex approximation. Simulation results show that as the number of antennas goes to large-scale, the proposed three methods can achieve a dramatic complexity reduction over conventional Root-MUISC. Particularly, the PSCC and PI-Max-CSCA can reach the CRLB while the PSAC shows a substantial performance loss.