This study introduces an efficient, frequency-dependent, adaptive method for determining Tikhonov regularization parameters in multi-zone sound field reproduction using a least-square-based technique. Unlike conventional methods that either iteratively select the regularization parameter or employ a fixed ratio of the largest eigenvalue of the transfer function, this approach combines the L-curve and Normalized Tikhonov to adaptively adjust the ratio to the largest eigenvalue in response to frequency changes. Simulation results confirm that the proposed Adaptive Normalized Tikhonov (ANT) method outperforms traditional approaches by enhancing efficiency and overall performance.