Showing papers in "Linear Algebra and its Applications in 2010"

TL;DR: A new interpolation formula is suggested in which a d -dimensional array is interpolated on the entries of some TT-cross (tensor train-cross) and the total number of entries and the complexity of the interpolation algorithm depend on d linearly, so the approach does not suffer from the curse of dimensionality.

TL;DR: A new algorithm for symmetric tensor decomposition is proposed, based on this characterization and on linear algebra computations with Hankel matrices, which permits an efficient computation of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence.

TL;DR: In this paper, a spectral graph theory based on the signless Laplacians Q and compare it with other spectral theories, in particular to those based on adjacency matrix A and the L-Laplacian L. This theory is called M-theory.

TL;DR: In this article, Kilmer et al. define a free module and show that every linear transformation on that module can be represented by tensor multiplication, and present a generalization of ideas of eigenvalue and eigenvector to the space of n × n-times-n tensors.

TL;DR: In this paper, an iterative method to solve the generalized coupled matrix equations over generalized bisymmetric matrix groups was proposed, where the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases were solved using the conjugate gradient method.

TL;DR: In this paper, the positive semidefinite zero forcing number Z(G) is introduced, which is the minimum number of vertices in a zero forcing set of a graph G, used to study the maximum nullity/minimum rank of the family of symmetric matrices described by G.

TL;DR: A survey of the basics of the theory of two projections can be found in this article, which contains the theorem by Halmos on two orthogonal projections and Roch, Silbermann, Gohberg, and Krupnik's theorem on two idempotents in Banach algebras.

TL;DR: A sharp upper bound for the skew energy of D is derived in terms of the order of D and the maximum degree of its underlying undirected graph, and an infinite family of digraphs attaining the maximum skew energy.

TL;DR: This paper considers the energy of a simple graph with respect to its normalized Laplacian eigenvalues, which is called the L-energy, and provides upper and lower bounds for L- energy based on its general Randic index R-1(G).

TL;DR: In this paper, the authors survey classical and some more recent results on the spectra of digraphs, equivalently, the (0, 1)-matrices, with emphasis on the spectral radius.

TL;DR: In this paper, it was shown that if G is a graph of order n and μ (G ) is the largest eigenvalue of its adjacency matrix, then G does not contain a Hamiltonian cycle unless G = K n - 1 + e + v.

TL;DR: In this paper, a lower bound on the second largest signless Laplacian eigenvalue and an upper bound for the smallest signless eigen value of a simple graph was given.

TL;DR: Two generalizations of the CUR matrix decomposition Y = CUR are provided to the case of N -way arrays (tensors) and an adaptive type algorithm for the selection of proper fibers in the FSTD1 model is provided which is useful for large scale applications.

TL;DR: The minimum rank problem for simple directed trees is solved and the maximum eigenvalue multiplicity of symmetric tree sign patterns is found.

TL;DR: In this paper, the maximum spectral radius of graphs without paths of given length, and tight bounds on the spectral radius for graphs without given even cycles, were given. And they also raised a number of open problems.

TL;DR: In this paper, the signless Laplacian spectral radius of a graph has been shown to be tight for the existence of Hamiltonian paths and cycles, and tight conditions on the spectral radius have been given for their existence.

TL;DR: In this article, the extremal inertias of the linear matrix expression A - BXB ∗ with respect to a variable Hermitian matrix X were derived, and some results were given for extremal solutions to the matrix equation AX = B.

TL;DR: Bounds for entries of matrix functions based on Gauss-type quadrature rules are applied to adjacency matrices associated with graphs to develop inexpensive and accurate upper and lower bounds for certain quantities that describe properties of networks.

TL;DR: In this paper, the authors show that the canonical dual is not necessarily the optimal dual for the erasure problem in a finite-dimensional Hilbert space, and they give sufficient conditions under which the Canonical dual is the unique optimal dual frame for the Erasure problem.

TL;DR: Balakrishnan et al. as discussed by the authors showed that for each ϵ > 0, there exist infinitely many such n that E ( G ) E 0 > 1 - ϵ.

TL;DR: Wehe et al. as mentioned in this paper studied the class of graphs for which Z(G ) = M F (G ) for some field F was introduced to bound the maximum nullity of G on n vertices and a field F.

TL;DR: In this article, the Ky Fan theorem is applied to the theory of graph energy, resulting in several new inequalities, as well as new proofs of some earlier known inequalities, in the case of graph adjacency matrices.

TL;DR: The Minkowski sum of edges corresponding to the column vectors of a matrix A with real entries is the same as the image of a unit cube under the linear transformation defined by A with respect to the standard bases as discussed by the authors.

TL;DR: In this article, it was shown that every nonlinear Lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero.

TL;DR: In this paper, the authors characterized the distance spectra of integral circulant graphs and proved that these graphs have integral eigenvalues of distance matrix D. They also presented two families of pairs (G1,G2) with equal distance energy, in the first family G1 is subgraph of G2 while in the second family the diameter of both graphs is three.

TL;DR: In this paper, the general form of commuting mappings of a class of generalized matrix algebras is described and the question of proper form of such mappings is investigated.

TL;DR: In this paper, it was shown that if the second largest eigenvalue of a d-regular graph G is less than ρ ( d ), then G is 2 -edge-connected.

TL;DR: In this paper, it was shown that for any positive integer m, n, s, t and k = 0, 1, s - 2, k - 2, k - 3, k-4, k-5, t - 6, t-1, t − 2, t-2, t−1, T-2, T-3, t + 1, t+1, t + 2, T + 1 2, t 2 + 1.

TL;DR: Numerically the efficiency of $\lun$ minimization for the recovery of sparse signals from compressed sampling measurements in the noiseless case is explored, and a greedy algorithm computes sparse vectors that are difficult to recover by $\ell_1$-minimization.

TL;DR: In this article, a hybrid APproximation solution (HAPS) is proposed to generate the Tykhonov regularized TLS solution, provided that some care is taken to do the updates properly.