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With the ongoing growth in radio communications, there is an increased contamination of radio astronomical source data, which hinders the study of celestial radio sources. In many cases, fast mitigation of strong radio frequency interference (RFI) is valuable for studying short lived radio transients so that the astronomers can perform detailed observations of celestial radio sources. The standard method to manually excise contaminated blocks in time and frequency makes the removed data useless for radio astronomy analyses. This motivates the need for better RFI mitigation techniques for array of size M antennas. Although many solutions for mitigating strong RFI improves the quality of the final celestial source signal, many standard approaches require all the eigenvalues of the spatial covariance matrix (R ∈ ℂ M × M ) of the received signal, which has O (M 3) computation complexity for removing RFI of size d where d ≪ M. In this work, we investigate two approaches for RFI mitigation, (1) the computationally efficient Lanczos method based on the Quadratic Mean to Arithmetic Mean (QMAM) approach using information from previously-collected data under similar radio-sky-conditions, and (2) an approach using a celestial source as a reference for RFI mitigation. QMAM uses the Lanczos method for finding the Rayleigh–Ritz values of the covariance matrix R , thus, reducing the computational complexity of the overall approach to O (d M 2). Our numerical results, using data from the radio observatory Long Wavelength Array (LWA-1), demonstrate the effectiveness of both proposed approaches to remove strong RFI, with the QMAM-based approach still being computationally efficient. [ABSTRACT FROM AUTHOR]