In this paper we study a Jacobi block matrix and the behavior of the limit of its entries when a perturbation of its spectral matrix measure by the addition of a Dirac delta matrix measure is introduced. © 2001 Elsevier Science Inc. All rights reserved.

For a Jacobi matrix J on l(Z+) with Ju(n) = an−1u(n− 1) + bnu(n) + anu(n+ 1), we prove that ∑

In this work, we consider block-Jacobi methods with Newton steps in each subspace search and prove their local quadratic convergence to a local minimum with non-degenerate Hessian under some orthogonality assumptions on the search directions. Moreover, such a method is exemplified for non-unitary joint matrix diagonalization, where we present a block-Jacobi-type method on the oblique manifold w...

In this paper we study the bivariate theta-series which can be attached to the complete weight enumerator of ternary codes. We give an injective homorphism between the ring of invariants of a certain matrix group and the ring of Jacobi modular forms. This generalizes to Jacobi forms a result of Brou% e and Enguehard [Ann. Sci. % Ecole Norm. Sup. 5 (4) (1972) 157–181] on classical modular forms....

A class of simple Jacobi-type algorithms for non-orthogonal matrix joint diagonalization based on the LU or QR factorization is introduced. By appropriate parametrization of the underlying manifolds, i.e. using triangular and orthogonal Jacobi matrices we replace a high dimensional minimization problem by a sequence of simple one dimensional minimization problems. In addition, a new scale-invar...

Interval iteration can be used, in conjunction with other techniques, for rigorously bounding all solutions to a nonlinear system of equations within a given region, or for verifying approximate solutions. However, because of overestimation which occurs when the interval Jacobian matrix is accumulated and applied, straightforward linearization of the original nonlinear system sometimes leads to...

A Jacobi matrix with an → 1, bn → 0 and spectral measure ν(x)dx + dνsing(x) satisfies the Szegő condition if

A monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. The basic Christoffel transformation with shift α transforms the monic Jacobi matrix associated with a measure dμ into the monic Jacobi matrix associated with (x − α)dμ. This transformation is known...

STABILITY AND SENSITIVITY OF DARBOUX TRANSFORMATION WITHOUT PARAMETER M. ISABEL BUENO AND FROILÁN M. DOPICO Abstract. The monic Jacobi matrix is a tridiagonal matrix which contains the parameters of the three-term recurrence relation satisfied by the sequence of monic polynomials orthogonal with respect to a measure. Darboux transformation without parameter changes a monic Jacobi matrix associa...

In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also compute multivariate hypergeometric functions, and offer both symbolic and numerical evaluations for all these quantities. We prove that all algorithms are wel...