An EVD Algorithm for Para-Hermitian Polynomial Matrices

Impact of source model matrix conditioning on PEVD algorithms

“…To extend the utility of the eigenvalue (EVD) and singular value decompositions (SVD) [1] to general broadband problems, a polynomial EVD (PEVD [2][3][4]) has been defined. Given a parahermitian R(z), the PEVD R(z) ≈Q(z)Λ(z)Q(z) ,…”

“…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).…”

“…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). For K < M , R(z) is guaranteed to be rank deficient, but when K ≥ M it is possible for R(z) to have full rank.…”

“…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.…”

“…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]). …”