We consider discrete Dirac systems as an approach to the study of corresponding block Toeplitz matrices, which in many ways completes famous via Szegő recurrences and matrix orthogonal polynomials. prove analog Christoffel–Darboux formula derive asymptotic relations for reproducing kernel (using Weyl–Titchmarsh functions systems). These are expressed also terms matrices. case rational (and GBDT...

Independent Components Analysis nds a linear transformation to variables which are maximally statistically independent. We examine ICA from the point of view of maximising the likelihood of the data. We elucidate how scaling of the unmixing matrix permits a \static" nonlinearity to adapt to various marginal densities. We demonstrate a new algorithm that uses generalised exponentials functions t...

where ti(eres) and fa{erea) are the first and second traces, respectively, of eres. The first forms in terms of the constants of multiplication arise from the isomorphism between the first and second matrices of the elements of A and the elements themselves. The second forms result from direct calculation of the traces of R(er)R(es) and S(er)S(es), R{ei) and S(ei) denoting, respectively, the fi...

A standard multiplication algorithm for square matrices is transformed into a distributed algorithm. Every transformation step is veriied within the reenement calculus. Some high-level rules of reenement that are used in the derivation are proved.

For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of practical and efficient structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block GaussSeidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely de...

Transformation of multiple-trait records that undergo sequential selection can be used with derivative-free algorithms to maximize the restricted likelihood in estimation of covariance matrices as with derivative methods. Data transformation with appropriate parts of the Choleski decomposition of the current estimate of the residual covariance matrix results in mixed-model equations that are ea...

We report a new transformation, the LogDet, that is consistent for sequences with differing nucleotide composition and that have arisen under simple but asymmetric stochastic models of evolution. This transformation is required because existing methods tend to group sequences on the basis of their nucleotide composition, irrespective of their evolutionary history. This effect of differing nucle...

In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matric...

Recent work in the characterization of structured matrices in terms of characteristic polynomials of principal submatrices is furthered in this paper. Some classical classes of matrices with quasiseparable structure include tridiagonal (related to real orthogonal polynomials) and banded matrices, unitary Hessenberg matrices (related to Szegö polynomials), and semiseparable matrices, as well as ...

We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a Bäcklund transformation and prove its basic properties: canonicity, commutativity and spectrality. The Bäcklund transformation can be also viewed as a discretized time dynamics. Two Lax matrices are used: of order 2 and of order 2n + 2, which are mutually...