System identification algorithms are utilized in many practical and theoretical applications such as parameter estimation of sj'stems, adaptive control and signal processing . Least squares algorithm is one of the most popular algorithms in system identification, but it has some drawbacks such as large time consumption and small convergence rates. In this thesis, Gauss-Seidel method is implemented on recursive least squares algorithm and convergence behaviors of the resultant algorithms are analyzed. .Also in standard recursive least squares algorithm the excitation of modes are monitored using data matrices and this algorithm is accordingly altered. A parallel scheme is proposed in this analysis for efficient computation of the modes. The simulation results are also presented.