Showing papers on "M-matrix published in 2006"
TL;DR: In this article, the authors consider linear equations y = Φx where y is a given vector in ℝn and Φ is a n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the solution x1of the 1-minimization problem is unique and equal to x0.
Abstract: We consider linear equations y = Φx where y is a given vector in ℝn and Φ is a given n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the following property holds: For every y having a representation y = Φx0by a coefficient vector x0 ∈ ℝmwith fewer than ρ · n nonzeros, the solution x1of the 1-minimization problem
is unique and equal to x0. In contrast, heuristic attempts to sparsely solve such systems—greedy algorithms and thresholding—perform poorly in this challenging setting. The techniques include the use of random proportional embeddings and almost-spherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices. © 2006 Wiley Periodicals, Inc.
2,735 citations
TL;DR: This paper quantifies the 'sufficient sparsity' condition, defining an equivalence breakdown point (EBP), and describes a semi-empirical heuristic for predicting the local EBP at this ensemble of 'typical' matrices with unit norm columns.
231 citations
104 citations
TL;DR: A sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches that, if the system is exponentially almost sure stable, there exists a finite m such that the criterion is satisfied.
92 citations
TL;DR: Under suitable conditions, this work proves the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences and generalizes the known fixed-point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non-symmetric algebraic Riccati equations.
Abstract: For the non-symmetric algebraic Riccati equations, we establish a class of alternately linearized implicit (ALI) iteration methods for computing its minimal non-negative solutions by technical combination of alternate splitting and successive approximating of the algebraic Riccati operators. These methods include one iteration parameter, and suitable choices of this parameter may result in fast convergent iteration methods. Under suitable conditions, we prove the monotone convergence and estimate the asymptotic convergence factor of the ALI iteration matrix sequences. Numerical experiments show that the ALI iteration methods are feasible and effective, and can outperform the Newton iteration method and the fixed-point iteration methods. Besides, we further generalize the known fixed-point iterations, obtaining an extensive class of relaxed splitting iteration methods for solving the non-symmetric algebraic Riccati equations. Copyright © 2006 John Wiley & Sons, Ltd.
71 citations
TL;DR: In this paper, the nonsymmetric algebraic Riccati equation XM12X+XM11+M22X+M21=0, where M11, M12, M21, M22 are real matrices of sizes n × n, n × m, m × n and m × m respectively, is an irreducible singular M-matrix with zero row sums.
52 citations
TL;DR: It is proved that the Euler method is convergent with strong order p = 1/2 and the MS-stable properties ofThe Euler scheme are studied.
33 citations
TL;DR: In this work, ''Good'' Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are proposed and analyzed and the behavior of the above preconditionsers to the Krylov subspace methods is studied.
23 citations
TL;DR: In this paper, a necessary and sufficient condition is established for ascertaining the absolute exponential stability for a class of finite delayed neural networks with connection matrices A having nonnegative off-diagonal elements, delayed feedback matrix A τ having non negative elements and strictly increasing and Lipschitz activation functions.
21 citations
TL;DR: Results obtained in this paper show that the convergence rate of Jacobi and Gauss–Seidel type methods can be increased by using the preconditioned method when A is an M -matrix.
12 citations
TL;DR: A convergence theorem of the improved modified Gauss–Seidel iterative method, referred to as the IMGS method, for H -matrices is presented and the range of parameters i with that of the parameter of the SOR iterative process is compared.
Abstract: In this paper, first we present a convergence theorem of the improved modified Gauss–Seidel iterative method, referred to as the IMGS method, for H -matrices and compare the range of parameters i with that of the parameter of the SOR iterative method. Then with a more general splitting, the convergence analysis of this method for an H -matrix and its comparison matrix is given. The spectral radii of them are also compared. Copyright q 2006 John Wiley & Sons, Ltd.
TL;DR: Gowda et al. as discussed by the authors proved the P-property for the Lorentz cone and presented some partial results in the general case on the product of Q-transformations defined on self-dual closed convex cones.
TL;DR: This paper applies the improving modified Gauss-Seidel method to H-matrix and its comparison matrix, with a more general splitting, and presents the corresponding convergence results and the comparison results of the spectral radius.
TL;DR: It is shown that the proconditioner increases the convergence rate of the PCG method and reduces the operation cost and Numerical results are also given.
TL;DR: In this paper, robust global exponential stability criteria are established in terms of fairly simple algebraic conditions, and an estimate of the decay rate of the solutions of such systems are also derived.
Abstract: This paper studies linear impulsive systems with varying time-delay and uncertainty. By using the method of Lyapunov functions and matrix inequalities, robust global exponential stability criteria are established in terms of fairly simple algebraic conditions. Estimate of the decay rate of the solutions of such systems are also derived. Some examples are given to illustrate the main results.
Journal Article•
TL;DR: In this paper, the relation between the spectrum of the system matrix of a positive linear system and the existence of a Luenberger type positive linear observer has been investigated, and it is shown that a system admits such observers only if the number of nonnegative real eigenvalues of a system matrix is at most one.
Abstract: This paper investigates the relation between the spectrum of the system matrix of a positive linear system and the existence of positive linear observers. We only consider single output case. It is shown that a positive linear system admits a Luenberger type positive linear observer only if the number of nonnegative real eigenvalues of the system matrix is at most one. Moreover, we provide a necessary condition on the existence of positive linear observers which employ a coordinates transformation and whose system matrices are diagonal.
Journal Article•
TL;DR: This paper pointed out that the conditions of some main results in "Practical criteria for H-matrices" are not necessary and improved the result by simple methods, and showed new judging methods of H -matrix are shown.
Abstract: In this paper, we point out that the conditions of some main results in "Practical criteria for H-matrices" are not necessary. By the simple methods, we improve the result. Moreover, new judging methods of H-matrix are shown.
01 Jan 2006
TL;DR: In this paper, the concept of locally α-bi-diagonally dominant matrices is used to present some equivalent representations for identifying generalized strictly diagonally superior matrices and thus the corresponding results are thus generalized.
Abstract: The concept of locally α-bi-diagonally dominant matrices is used to present some equivalent representations for identifying generalized strictly diagonally dominant matrices and thus the corresponding results are thus generalized.
01 Jul 2006
TL;DR: In this paper, a comparing model is introduced to transfer the problem of output feedback for stabilizing the Lurie composited nonlinear systems into output feedback stabilising the comparison systems of lower dimensions.
Abstract: A comparing model is introduced to transfer the problem of output feedback for stabilizing the Lurie composited nonlinear systems into output feedback stabilizing the comparison systems of lower dimensions, by employing differential and Lyapunov stability theory integrally A stability condition is developed in form of M matrix, the corresponding LMI expression is founded, which leads to an iterative approach to obtain the output feedback gain An algorithm to obtain the output-feedback gain matrix is developed here based on the LMI technique The key technique of developing iterative law of the matrix variable existing in QMI is discussed also The character of the results proposed here is decreasing complexity Finally, a numerical example is given to illustrate our results and its application