Several past algorithms for eigenvalue based on digital signal processing

The finite difference time domain (FDTD) method has been proved to be one of the most prominent computer tools for solving the Maxwell's equation, and applied for many fields of electromagnetism, but it always has its difficulty in dealing with a resonant circuit because of the accumulating and releasing of energy in the resonator. For the sake of improving the efficiency, the MUSIC algorithm has been utilized to exploit the eigenvalue decomposition of the correlation matrix of the signal to implement a fast FDTD analysis of a resonant circuit. Because of matrix computation which is troublesome when the matrix is ill-conditioned, application of MUSIC algorithm is limited. In this paper, the Marple algorithm and learning algorithm are introduced to develop two novel fast FDTD analysis algorithms. It has been proved both analytically and by simulation results that the weight vector provided by the proposed learning algorithm is guaranteed to converge to the minor component of the input signals. The difference among the three algorithms including the extant MUSIC algorithm is discussed. Using the three algorithms, a resonant structure with a dielectric resonator (DR) and microstrip is analyzed and the same resonant frequency is obtained.