Showing papers in "Linear Algebra and its Applications in 2000"

TL;DR: In this paper, the authors focus on the inverse problem: given the system as a whole, identify the almost invariant aggregates together with the (small) probabilities of transitions between them.

TL;DR: In this article, the authors developed normwise backward errors and condition numbers for the polynomial eigenvalue problem, and showed that solving the QEP by applying the QZ algorithm to a corresponding generalized eigen value problem can be backward unstable.

TL;DR: Borders on the existence of rank-revealing LU factorizations that are comparable with those of rank -revealing QR factorizations are presented, and an algorithm using only Gaussian elimination for computing rank- RevealingLU factorizations is introduced.

TL;DR: For positive semi-definite n×n matrices, the inequality 4|||AB|||⩽|||(A+B) 2||| isshown to hold for every unitarily invariant norm as discussed by the authors.

TL;DR: In this paper, an alternating minimization (AM) procedure is used to find a local minimum of the objective function, which is then used to fix either the blur or the image and minimize respect to the other variable, each step is a standard non-blind deconvolution problem.

TL;DR: Theoretical properties of eigenfunctions of selected incidence matrices appearing in spatial statistics formulae are summarized in this article, and seven theorems are proposed and proved, and three conjectures are posited.

TL;DR: In this article, several general techniques on linear preserver problems are described, based on a transfer principle in Model Theoretic Algebra that allows one to extend linear preservers results on complex matrices to matrices over other algebraically closed fields of characteristic 0.

TL;DR: In this article, the authors consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings, and construct Belitskii's algorithm for reducing a matrix to a canonical form, which is the generalization of the Jordan normal form.

TL;DR: In this article, the convergence analysis for modified Gauss-Seidel and Jacobi type iterative methods is presented and a comparison of spectral radius among the Gauss -Seidel iterative method and these modified methods is provided.

TL;DR: The principal pivot transform (PPT) as discussed by the authors is a transformation of the matrix of a linear system to exchange unknowns with the corresponding entries of the right-hand side of the system.

TL;DR: In this article, the sensitivity of the stationary probabilities for an n -state, time-homogeneous, irreducible Markov chain in terms of the mean first passage times in the chain was analyzed.

TL;DR: The behavior of iterative methods of GMRES-type when applied to singular, possibly inconsistent, linear systems is discussed and conditions under which these methods converge to the least-squares solution of minimal norm are presented.

TL;DR: This work suggests efficient implementations for three nonnegatively constrained restorations schemes: constrained least squares, maximum likelihood and maximum entropy, and shows that with a certain parameterization, and using a Quasi-Newton scheme, these methods are very similar.

TL;DR: In this article, it was shown that ∥ 1 p A p X+ 1 q XB q ∥ 2 2 ⩾ 1 r 2 A p x−XB q 2 2 + AXB 2 2, where r=max(p,q) and · 2 is the Hilbert-Schmidt norm.

TL;DR: The characteristic equation for the spectrum is given and it is shown that the spectrum depends only on the structure of the graph and the asymptotic behaviour of the eigenvalues is investigated by proving the so-called Weyl's formula.

TL;DR: In this article, it was shown that the spectral geometric mean of positive definite matrices X and Y is similar to the square of the matrix product XY 2 X∼YX 2 Y.

TL;DR: In this paper, it was shown that T n is an IAP for all n⩾2, and the truth of the conjecture was extended to n ⩽7.

TL;DR: The inner perturbations induced by Δ1 are studied and it is proved that as τ→λj the smallest eigenvalue has relative condition number relcond=1+O(|τ−λj|), which is a rational function of τ.

TL;DR: In this article, the relationship between the k-Fibonacci sequence and ln(k) and 1-factors of a bipartite graph was investigated for a positive integer k⩾2.

TL;DR: In this article, it was shown that the set of all commuting d -tuples of commuting n×n matrices that are contained in an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of the irreduciblity of the variety of commuting pairs.

TL;DR: In this paper, the spectral norm of the Hadamard product of two n×m matrices A and B is shown to be bounded by a constant factor κ(·) for a real non-singular matrix X and invertible diagonal matrices D,E.

TL;DR: In this article, a complete solution is established to the problem of characterizing all situations, where a linear combination of two different idempotent matrices P 1 and P 2 is also an idemomorphent matrix.

TL;DR: The issues that have to be faced when the dqds algorithm is to be realized on a computer are discussed: criteria for accepting a value, for splitting the matrix, and for choosing a shift to reduce the number of iterations as well as the relative advantages of using IEEE arithmetic when available.

TL;DR: In this article, a moment map condition in Hamiltonian geometry has been proposed for solving Horn's problem, which can be used in linear algebra and can be seen as a generalization of geometric invariant theory.

TL;DR: Wei et al. as mentioned in this paper characterize matrices B such that B π =A π, and derive from the results: (1) error bounds for the Drazin inverse of a perturbation, (2) improvement of error bounds given recently by Wei [10], Wei and Wang [11] and Castro Gonzalez et al., and (3) a new characterization of EP matrices.

TL;DR: In this paper, a lower bound for the second smallest eigenvalue of Laplacian matrices in terms of the isoperimetric number of weighted graphs is given. But this lower bound is not applicable to the real parts of the nonmaximal eigenvalues of irreducible nonnegative matrices.

TL;DR: Using harmonic analysis on symmetric spaces, this paper showed that the singular spectral problem for products of matrices can be reduced to the problem for sums of Hermitian matrices.

TL;DR: This paper corrected an error in the proof of the main result of the authors' paper "Orthogonal Representations and Connectivity of Graphs" which appeared in Linear Algebra and its Applications 114/115 (1989) 439-454.

TL;DR: In this paper, the general Hermitian nonnegative-definite solution to the matrix equation AXA ∗ = B is established in a form which can be viewed as a corrected version of that derived by C.G. Khatri and S.K. Mitra.

TL;DR: The LU factorization of the Vandermonde matrix is obtained, using complete symmetric functions, and the lower and upper triangular matrices are factorized into 1-banded matrices, thus expressing the Vander Redmonde matrix as a product of 1- banded matrix.