scispace - formally typeset
Search or ask a question

Showing papers in "Linear Algebra and its Applications in 2006"


Journal ArticleDOI
TL;DR: This paper develops an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes.

598 citations


Journal ArticleDOI
TL;DR: An identity for additive modivations of a singular value decomposition (SVD) to reflect updates, downdates, shifts, and edits of the data matrix is developed to set the stage for fast and ememory-efficient sequential algorithms for tracking singular values and subspaces.

509 citations


Journal ArticleDOI
TL;DR: In this paper, the Laplacian energy of a graph G with n vertices and m edges is defined and investigated as LE(G)=∑i=1n|μi-2m/n|.

435 citations


Journal ArticleDOI
TL;DR: The geometric mean of two positive definite matrices has been defined in several ways and studied by several authors, including Pusz and Woronowicz, and Ando.

260 citations


Journal ArticleDOI
TL;DR: In this paper, the existence and nonexistence of solutions for NP-hard equations involving absolute values of variables were investigated, where A is an arbitrary n ǫ×ǫ n real matrix.

243 citations


Journal ArticleDOI
TL;DR: The uniqueness of the dictionary A is established, depending on the quantity and nature of the set { b i }, and the sparsity of { x i }, and a recently developed algorithm is described that practically find the matrix A, in a manner similar to the K-Means algorithm.

227 citations


Journal ArticleDOI
TL;DR: Two methods for solving the problem of order reduction of large-scale linear time invariant systems by using Krylov subspace methods via first-order models, resulting in an even higher number of matching moments.

198 citations


Journal ArticleDOI
TL;DR: Three algorithms for the model reduction of large-scale, continuous-time, time-invariant, linear, dynamical systems with a sparse or structured transition matrix and a small number of inputs and outputs are described.

153 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extend the theory of nonnegative matrices to the matrices that have some negative entries, and propose the Perron-Frobenius splitting for the solution of the linear system Ax = b.

139 citations


Journal ArticleDOI
TL;DR: In this article, a Krylov subspace based projection method is presented for model reduction of large scale bilinear systems, which matches a desired number of moments of multivariable transfer functions corresponding to the kernels of Volterra series representation of the original system.

135 citations


Journal ArticleDOI
TL;DR: This paper proves that the GLT class is closed under inversion as well when the sequence which is inverted shows a sparsely vanishing symbol, and demonstrates that the results on GLT sequences can be used in a PDE setting in various directions.

Journal ArticleDOI
TL;DR: A new method for constructing a reduced system by preserving the second-order structure of the original system is presented, using a variant of the well-known balanced truncation technique applied to second- order gramians.

Journal ArticleDOI
TL;DR: In this article, the authors analyze and expand a recently developed approach to model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear (TPWL) approximations.

Journal ArticleDOI
TL;DR: In this article, the authors proposed Krylov subspace methods for solving large Lyapunov matrix equations of the form AX+XAT+BBT = 0, where A and B are real n× n and n× s matrices, respectively, with s ≥ n.

Journal ArticleDOI
TL;DR: In this article, a variant of Jensen's operator inequality for convex functions, which is a generalization of Mercer's result, is proved and used to prove a monotonicity property for Mercer's power means for operators.

Journal ArticleDOI
TL;DR: In this article, the authors consider higher-rank versions of the standard numerical range for matrices, and develop the basic structure theory for the higher rank numerical ranges, and give a complete description in the Hermitian case.

Journal ArticleDOI
TL;DR: In this paper, the Constrained Total Least Squares Estimate (CTLSE) can be generated by solving a certain sequence of eigenvalue problems iteratively, where the normal matrix from the constrained (standard) least squares approach has to be suitably augmented by one row and one column.

Journal ArticleDOI
TL;DR: In this article, it was shown that the induced subgraphs on the set of all non-scalar non-invertible, nilpotent, idempotent and involution matrices in the commuting graph of a division ring can be computed.

Journal ArticleDOI
TL;DR: Canonical forms for congruence and ∗congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347-353] as discussed by the authors.

Journal ArticleDOI
TL;DR: In this paper, the authors derived the probability density function and the probability distribution function of the largest canonical angle between two p-dirnensional subspaces of R-n chosen from the uniform distribution on the Grassmann manifold.

Journal ArticleDOI
TL;DR: In this article, it was shown that every Jordan derivation of triangular algebras is a derivation, which is the same as the derivation in the present paper.

Journal ArticleDOI
TL;DR: This paper interprets the NMF algorithm as an alternating minimization procedure a la Csiszar–Tusnady and investigates some of its stability properties, including the connections between NMF and Archetypal Analysis.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the inequalities w q + r (G) w q (G ) ⩽ μ r ( G ) w q(G) ⩾ μ r(G )⩽ ω ( G) -1 ω( G ) - 1 ω g ) w r (g) w r(g ) hold for all r ≥ 0 and odd q ≥ 0.

Journal ArticleDOI
Yuming Shi1
TL;DR: In this paper, the authors established the Weyl-Titchmarsh theory for a class of discrete linear Hamiltonian systems over a half-line and derived the defect indices of the minimal operator.

Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition for the existence of a diagonal common quadratic Lyapunov function (CQLF) for a pair of positive linear time-invariant (LTI) systems was derived.

Journal ArticleDOI
TL;DR: In this paper, the mixing time of a Markov chain was studied and a measure of mixing time in a finite irreducible discrete-time Markov Chain was proposed, where mixing time is defined as the first passage time from state i to state j of the chain.

Journal ArticleDOI
TL;DR: In this article, a new realizability criterion for the real nonnegative inverse eigenvalue problem (NIEP) was proposed, which is not contained in Soto's criterion.

Journal ArticleDOI
TL;DR: In this article, the generalized Drazin inverse of the sum a ǫ+ǫ b could be expressed in terms of a, a d, b, b d, a c, b c, b c, c c, c c, a c, a b, c d, b b c.

Journal ArticleDOI
TL;DR: The application of balanced truncation model reduction to the semidiscretized Stokes equation is demonstrated and it is demonstrated that the asymptotic stability is preserved in the reduced order system and there is an a priori bound on the approximation error.

Journal ArticleDOI
TL;DR: This paper presents a cache oblivious algorithm for matrix multiplication that uses a block recursive structure and an element ordering that is based on Peano curves that leads to an asymptotically optimal spatial and temporal locality of the data access.