Since a number of signal processing algorithms requiring the EVD of a symmetric matrix are implemented on fixedpoint DSPs, there is considerable interest in matrix diagonalization algorithms that can be implemented in fixed-point arithmetic. We propose modifications to the Jacobi Cyclic Row algorithm that favor a fixed-point implementation. We then compare the eigenvalues and eigenvectors obtai...

In this paper, we focus on the fourth order cumulant based adaptive methods for independent component analysis. We propose a novel method based on the Jacobi Optimization, available for a wide set of minimum entropy (ME) based contrasts. In this algorithm we adaptively compute a moment matrix, an estimate of some fourth order moments of the whitened inputs. Starting from this matrix, the soluti...

We study the double scaling limit for unitary invariant ensembles of randommatrices with non analytic potentials and find the asymptotic expansion for the entries of the corresponding Jacobi matrix. Our approach is based on the perturbation expansion for the string equations. The first order perturbation terms of the Jacobi matrix coefficients are expressed through the Hastings-McLeod solution ...

A new complex Jacobi iterative technique adapted for the solution of three-dimensional (3D) wide-angle (WA) beam propagation is presented. The beam propagation equation for analysis of optical propagation in waveguide structures is based on a novel modified Padé(1,1) approximant operator, which gives evanescent waves the desired damping. The resulting approach allows more accurate approximation...

The matrix volume is a generalization, to rectangular matrices, of the absolute value of the determinant. In particular, the matrix volume can be used in change-of-variables formulæ, instead of the determinant (if the Jacobi matrix of the underlying transformation is rectangular). This result is applicable to integration on surfaces, illustrated here by several examples. SIAM J. Matrix Analysis...

The main aim of this paper is to construct a multivariable extension with the help of the extended Jacobi matrix polynomials (EJMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented.

Multimode/multicore fibers are expected to provide an attractive solution to overcome the capacity limit of current optical communication system. In presence of high crosstalk between modes/cores, the squared singular values of the input/output transfer matrix follow the law of the Jacobi ensemble of random matrices. Assuming that the channel state information is only available at the receiver,...

Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x as well as for the ki...

We study a stepwise algorithm for solving the indefinite truncated moment problem and obtain the factorization of the matrix describing the solution of this problem into elementary factors. We consider the generalized Jacobi matrix corresponding to Magnus’ continuous P -fraction that appears in this algorithm and the polynomials of the first and second kind that are solutions of the correspondi...

We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determines H). We prove an extension of Hochstadt’s theorem (who proved the result in the case n = N) that n eigenvalues of an N ×N Jacobi matrix, H, can replace the first n matrix elements in determining H uniq...