Neural Networks for Computing Eigenvalues of Parahermitian Matrices

Calculating the eigenvalues and eigenvectors of a polynomial matrix has proved to be an important problem in signal processing, in recent years. There exists various iterative algorithms for approximating the polynomial eigenvalue decomposition (PEVD), such as the sequential matrix diagonalisation (SMD). In this paper, we propose two artificial neural network (ANN)-based approaches to computing the polynomial eigenvalues found by the SMD. This is achieved via a feed-forward and convolutional neural network models that are trained using SMD-based eigenvalues. Simulated results highlight ANN-based PEVD computation as a viable alternative to using iterative PEVD algorithms. Results show favourable computational efficiency of the proposed CNN approach compared to the SMD algorithm, whilst achieving high eigenvalue-estimation accuracy.a