Efficient Implementation of Iterative Polynomial Matrix EVD Algorithms Exploiting Structural Redundancy and Parallelisation

A number of algorithms are capable of iteratively calculating a polynomial matrix eigenvalue decomposition (PEVD), which is a generalisation of the EVD and will diagonalise a parahermitian polynomial matrix via paraunitary operations. While offering promising results in various broadband array processing applications, the PEVD has seen limited deployment in hardware due to the high computational complexity of these algorithms. Akin to low complexity divide-and-conquer (DaC) solutions to eigenproblems, this paper addresses a partially parallelisable DaC approach to the PEVD. A novel algorithm titled parallel-sequential matrix diagonalisation exhibits significantly reduced algorithmic complexity and run-time when compared with existing iterative PEVD methods. The DaC approach, which is shown to be suitable for multi-core implementation, can improve eigenvalue resolution at the expense of decomposition mean squared error, and offers a trade-off between the approximation order and accuracy of the resulting paraunitary matrices.