In many data-intensive applications, the use of principal component analysis and other related techniques is ubiquitous for dimension reduction, data mining, or other transformational purposes. Such transformations often require efficiently, reliably, and accurately computing dominant singular value decompositions (SVDs) of large and dense matrices. In this paper, we propose and study a subspace optimization technique for significantly accelerating the classic simultaneous iteration method. We analyze the convergence of the proposed algorithm and numerically compare it with several state-of-the-art SVD solvers under the MATLAB environment. Extensive computational results show that on a wide range of large unstructured dense matrices, the proposed algorithm can often provide improved efficiency or robustness over existing algorithms.