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A comparative study of approximate joint diagonalization algorithms of a set of matrices is presented. Using a weighted least-squares criterion, without the orthogonality constraint, an algorithm is compared with an analogous one for blind source separation (BSS). The criterion of the present algorithm is on the separating matrix while the other is on the… (More)

This paper deals with the problem of blind separation of an instantaneous mixture of Gaussian autoregressive sources, without additive noise, by the exact maximum likelihood approach. The maximization of the likelihood function is divided, using relaxation, into two suboptimization problems, solved by relaxation methods as well. The first one consists of… (More)

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison… (More)

— A new algorithm for approximate joint diagonal-ization of a set of matrices is presented. Using a weighted least-squares (WLS) criterion, without the orthogonality constraint, it is compared with an analoguous algorithm for blind source separation (BSS). The criterion of our algorithm is on the separating matrix while the other is on the mixing matrix.… (More)

This paper presents the problem of maximizing the determinant of a K-square real matrix B, subject to the constraint that each row b k of B satisfies b t k Γ k b k ≤ 1, where Γ 1 ,. .. , Γ K , are K given real symmetric positive definite matrices. Existence and uniqueness of the solution is discussed. An iterative algorithm, using a method of relaxation… (More)

— We present in this paper a non-orthogonal algorithm for the approximate joint diagonalization of a set of matrices. It is an iterative algorithm, using relaxation technique applied on the rows of the diagonalizer. The performances of our algorithm are compared with usual standard algorithms using blind sources separation simulations results. We show that… (More)