Efficient Eigenvalue Computation of Parahermitian Matrices Using Neural Networks

In recent years, computing the eigenvalue decomposition of a polynomial matrix has become increasingly essential in many areas of adaptive signal processing. However, traditional iterative algorithms, such as sequential matrix diagonalisation (SMD), often incur high computational costs. This paper proposes two artificial neural network (ANN)-based approaches for computing polynomial eigenvalues estimated by the SMD. By utilizing feed-forward and convolutional neural network models, we significantly reduce computational costs, including CPU time and floating-point operations per second (FLOPS). The results demonstrate that ANN-based polynomial eigenvalue decomposition (PEVD) offers a more efficient solution for large matrix computations compared to traditional methods.