Abstract-A polynomial eigenvalue decomposition of parahermitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.
In this paper, we show that the paraunitary (PU) matrices that arise from the polynomial eigenvalue decomposition (PEVD) of a parahermitian matrix are not unique. In particular, arbitrary shifts (delays) of polynomials in one row of a PU matrix yield another PU matrix that admits the same PEVD. To keep the order of such a PU matrix as low as possible, we pro- pose a row-shift correction. Using the example of an iterative PEVD algorithm with previously proposed truncation of the PU matrix, we demonstrate that a considerable shortening of the PU order can be accomplished when using row-corrected truncation
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Abstract-A number of algorithms for the iterative calculation of a polynomial matrix eigenvalue decomposition (PEVD) have been introduced. The PEVD is a generalisation of the ordinary EVD and will diagonalise a parahermitian matrix via paraunitary operations. This paper addresses savings -both computationally and in terms of memory use -that exploit the parahermitian structure of the matrix being decomposed, and also suggests an implicit trimming approach to efficiently curb the polynomial order growth usually observed during iterations of the PEVD algorithms. We demonstrate that with the proposed techniques, both storage and computations can be significantly reduced, impacting on a number of broadband multichannel problems.
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