Showing papers in "Linear Algebra and its Applications in 2014"

TL;DR: This algorithm is the first block Kaczmarz method with an (expected) linear rate of convergence that can be expressed in terms of the geometric properties of the matrix and its submatrices.

TL;DR: The present paper reports on the results related to the distance matrix of a graph and its spectral properties.

TL;DR: In this article, it was shown that approximately sparse signals that are not extremely sparse can be accurately reconstructed from single-bit measurements sampled according to a sub-gaussian distribution, and the reconstruction comes as the solution to a convex program.

TL;DR: In this article, the core and dual core inverse are extended from matrix to an arbitrary ⁎-ring case, and several characterizations of these inverses are given.

TL;DR: This work proposes a new family of pursuit algorithms for the cosparse analysis model, mimicking the greedy-like methods – compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) andhard thresholding pursuit (HTP).

TL;DR: The notion of matrix polynomials has been studied in the context of matrix matrix functions as mentioned in this paper, where it is shown that the sum of the (finite and infinite) partial multiplicities, together with the (left and right) minimal indices of any matrix function is equal to the rank times the degree of the function.

TL;DR: In this article, the robust null space property and the quotient property were used to prove that the equality-constrained l 1 -minimization remains stable and robust.

TL;DR: In this paper, the Randic matrix R = ( r i j ) of a graph G whose vertex v i has degree d i is defined by R i j = 1 / d i d j if the vertices v i and v j are adjacent and r i J = 0 otherwise.

TL;DR: This paper shows that a symmetric B tensor can always be decomposed to the sum of a strictly diagonally dominated symmetric M tensor and several positive multiples of partially all one tensors.

TL;DR: This paper establishes bounds on the number of required measurements in the anisotropic case, where the ensemble of measurement vectors possesses a non-trivial covariance matrix and finds that the required sampling rate grows proportionally to the condition number of the covariance Matrix.

TL;DR: It is shown that phase retrieval from M+1 almost injective intensity measurements is NP-hard, indicating that computationally efficient phase retrieval must come at the price of measurement redundancy.

TL;DR: In this article, the authors proposed a matrix theory construction allowing to deduce the Markovian analog of the Berger-Wang formula from the classical BWC, which is valid for the case of Markovians analogs of the joint and the generalized spectral radii too.

TL;DR: In this paper, it was shown that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k ⩾ 3, reaches its upper bound 2 Δ ( G ), where Δ (G ) is the largest degree of G, if and only if G is regular.

TL;DR: In this paper, the rank of a uniform hypergraph is independent of the ordering of its vertices and the Laplacian tensor has the same rank for odd-bipartite even-uniform hypergraphs.

TL;DR: In this article, it was shown that for an m-order n-dimensional Hilbert tensor (hypermatrix) H ∞ = (H i 1 i 2 ⋯ i m ) the spectral radius is not larger than n m − 1 sin π n, and an upper bound of its E-spectral radius is n m 2 sin ρ n.

TL;DR: In this article, the authors extend previous results on the exponential off-diagonal decay of the entries of analytic functions of banded and sparse matrices to the case where the matrix entries are elements of a C ⁎ -algebra.

TL;DR: It is proved that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension.

TL;DR: In this article, it was shown that λ n estimates how much Γ is far from being balanced, where n is the frustration number (resp. frustration index), that is the minimum number of vertices to be deleted such that the signed graph is balanced.

TL;DR: In this article, the spectral theory of 2-graphs is extended to weighted uniform hypergraphs, and the eigenvalues-numbers λ and λ min are extended to eigen values-functions λ ( p ) and ǫ min (ǫ ), which also encompass other graph parameters like the Lagrangian and the number of edges.

TL;DR: In this article, a Jensen operator inequality for superquadratic functions is presented, where the Jensen inequality is extended to super-quadratic functions and some applications for their applications are discussed.

TL;DR: The subdivision graph S (G) of a graph G is the graph obtained by inserting a new vertex into every edge of G as discussed by the authors, where I (G 1 ) is the set of inserted vertices of S ( G 1 ).

TL;DR: This paper answers three questions about P, P 0, B and B 0 tensors and obtains further results about P , P 0 , B andB 0 Tensors.

TL;DR: In this article, a generalization of M. Slocinski's Wold decomposition of a pair of doubly commuting isometries on Hilbert spaces is presented, where the main result is a several variables analogue of the decomposition.

TL;DR: In this paper, it was shown that the complete multipartite graphs are determined by their distance spectra, which confirms the conjecture proposed by Lin, Hong, Wang and Shu.

TL;DR: In this article, the authors describe a flag of vector spaces (i.e., a nested sequence of vectors spaces) that best represents a collection of subspaces of different dimensions.

TL;DR: In this article, it was shown that for any self-adjoint matrix A of rank k, one has Det 2 ( A ) = ∑ P det 2 (A P ), where det ( A P ) runs over k × k minors of A and the sum on the right is taken over all minors P, understanding the sum to be 1 if | P | = 0.

TL;DR: In this article, the authors present the Fredholm theory on l p -spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra.

TL;DR: In this paper, it was shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has the similar property like that of a Fiedler vector.

TL;DR: This paper derives an elementary proof of Connelly’s sucient condition for universal rigidity of tensegrity frameworks and investigates the links between these two sucient conditions.

TL;DR: In this article, rank, border rank, catalecticant rank, generalized rank, scheme length, border scheme length and smoothable rank were introduced for symmetric tensors.