Abstract: The dominant mode rejection (DMR) beamformer is widely used in array signal processing because of its good ability to detect weak targets, few snapshots needed, and fast convergence speed. The computation of the DMR algorithm mainly lies in the feature decomposition of the covariance matrix of the data. As the number of elements increases, the computational will increase sharply. In addition, the setting of dimension parameters for the dominant mode subspace can also affect the performance of the algorithm. Starting from the perspective of Krylov subspace and utilizing the concepts of Lanczos type iteration and random approximation, the fast decomposition of the main mode subspace can be achieved to address the issues of increased computational complexity and dimension estimation of the main mode subspace. At the same time, the dimension of the main mode space can be verified and estimated during the Lanczos recursion process. The proposed method significantly reduces the computation of the algorithm, while also accurately estimating the dimensionality of the main mode space to improve algorithm performance. The effectiveness of the proposed algorithm is verified by simulation and experimental data analysis in this paper.