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Adaptive algorithms can be an important component of a sparse reconfigurable adaptive filter (SRAF) for photonic switches. In this paper, we propose a modified system-based (MSB) algorithm that not only has good performance for white and non-white input signals, but also has a reduced computational complexity compared with conventional approaches such as the previous cross-correlation-based (CCB) and system-based (SB) algorithms. In order to improve the convergence rate of the system, the MSB algorithm separately updates each row or column of the switch weight matrix. We also consider a specific structure for the intermediate desired signals, and present a computer simulation example to demonstrate the performance of the proposed SRAF algorithm for a system identification application.