Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices

Redif, Soydan; Weiss, Stephan; McWhirter, J.G.

doi:10.1109/tsp.2014.2367460

Cited by 101 publications

(224 citation statements)

References 17 publications

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“…The current most popular PEVD algorithms [4,[8][9][10] have the goal of diagonalising a parahermitian matrix R(z) starting from an initial approximation S (0) (z). The ith iteration of all algorithms consists of three common steps operating on S (i−1) (z), which vary with implementation.…”

Section: General Anatomymentioning

confidence: 99%

“…A number of PEVD algorithms have been introduced [4,[6][7][8][9][10], and offer various performance characteristics. The algorithms in [4,6,10] have been demonstrated on parahermitian matrices R(z) ∈ C M×M derived from random A(z) ∈ C M×K as R(z) = A(z)Ã(z).…”

Section: Introductionmentioning

confidence: 99%

“…IV.B.3 in [8]). In [9], a source model convolutively mixes spectrally majorised sources by means of an arbitrary paraunitary matrix, such that the ground truth PEVD with finite order factors and equality in (1) is guaranteed. Since these publications [4,[6][7][8][9][10] use differently conditioned problems, a direct comparison between algorithms proposed in individual papers is not always straightforward.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we generalise the source model idea in [9] to carefully control the conditioning of the parahermitian matrix. This includes a definition of the dynamic range of the underlying source, which can be linked to the condition number or eigenvalue spread of a parahermitian matrix by generalisation from the field of scalar matrices.…”

Section: Introductionmentioning

confidence: 99%

“…An ensemble of randomised parahermitian matrices with different dynamic ranges and types of majorisation are factorised by a number of PEVD algorithms belonging to the second order sequential best rotation (SBR2 family, [4,8] and the sequential matrix diagonalisation (SMD family, [9,10]). …”

Section: Introductionmentioning

confidence: 99%

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2nd IET International Conference on Intelligent Signal Processing 2015 (ISP)

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Polynomial parahermitian matrices can accurately and elegantly capture the space-time covariance in broadband array problems. To factorise such matrices, a number of polynomial EVD (PEVD) algorithms have been suggested. At every step, these algorithms move various amounts of off-diagonal energy onto the diagonal, to eventually reach an approximate diagonalisation. In practical experiments, we have found that the relative performance of these algorithms depends quite significantly on the type of parahermitian matrix that is to be factorised. This paper aims to explore this performance space, and to provide some insight into the characteristics of PEVD algorithms.

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Section: General Anatomymentioning

confidence: 99%