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Spectral-type subspace clustering algorithms have attracted wide attention because of their excellent performance displayed in a great deal of applications in machine learning domain. It is critical for spectral-type subspace clustering algorithms to obtain suitable coefficient matrices which could reflect the subspace structures of data sets. In this paper, we propose a latent block diagonal representation clustering algorithm (LBDR). For a data set, the goal of LBDR is to construct a block diagonal and dense coefficient matrix and settle the noise adaptively within the original data set by using dimension reduction technique concurrently. In brief, by seeking the solution of a joint optimization problem, LBDR is capable of finding a suitable coefficient matrix and a projection matrix. Furthermore, a series of experiments conducted on several benchmark databases show that LBDR dominates the related methods. [ABSTRACT FROM AUTHOR]

The coefficient matrix and local unitary (LU) transformation invariant of three-qubit states are studied in this paper. There is general relation between the coefficient matrix and independent LU transformation invariant existing which is shown. Especially, the three coefficient matrix can completely determine six algebraically independent local invariants for three-qubit pure states. [ABSTRACT FROM AUTHOR]

• Second-order displacement fields at liquid–solid interface. • Solution of wave equations based on velocity potentials. • Comparison between complete solution and special solution of displacements. • Sharply mutation of displacements at certain angle. • Different effect of interface on the second-order displacements. Based on the second-order harmonic potential theory, the characteristics of the second-order harmonic field generated at the solid–liquid interface induced by P wave incidence are analyzed. A planar model of the solid–liquid interface is established to study the variation of the second-order displacement field versus the incident angles. The homogeneous solution coefficient matrix, refraction and reflection coefficient matrix are introduced. According to the boundary conditions and Lagrange's various parameters method, the second-order displacement field is obtained, and its dependence on the solid–liquid interface is investigated. The different effects of boundary on the tangential displacement and normal displacement are demonstrated. Numerical simulation shows that the complete solution varies slightly at the incident angle, and the tangential displacement and the normal displacement change sharply at a mutation angle θ ω due to the boundary effect. [ABSTRACT FROM AUTHOR]

The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result. In this paper, we present such a proof by constructing a planar network allowing negative weights, applying the Lindström-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths. • Providing a combinatorial proof of the Hankel total positivity of type B Narayana polynomials. • Allowing negative weights in the construction of planar networks. • Establishing an elegant sign-reversing involution on families of nonintersecting lattice paths. [ABSTRACT FROM AUTHOR]

In this article, we obtain monomial bases for littleq-Schur algebras at even roots of unity. [ABSTRACT FROM PUBLISHER]

Solvers for linear systems with tridiagonal coefficient matrices sometimes employ direct methods such as the Gauss elimination method or the cyclic reduction method. In each step of the cyclic reduction method, nonzero offdiagonal entries in the coefficient matrix move incrementally away from diagonal entries and eventually vanish. The steps of the cyclic reduction method are generalized as forms of the stride reduction method. For example, the 2-stride reduction method coincides with the 1st step of the cyclic reduction method which transforms tridiagonal linear systems into pentadiagonal systems. In this paper, we explain arbitrary-stride reduction for linear systems with coefficient matrices with three nonzero bands. We then show that arbitrary-stride reduction is equivalent to a combination of 2-stride reduction and row and column permutations. We thus clarify eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction method. We also provide two examples verifying this property. [ABSTRACT FROM AUTHOR]

Consider an infinite dimensional vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite-dimensional vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance-covariance matrix has the same convergence rate as that in case of i.i.d. samples. [ABSTRACT FROM AUTHOR]

A common mesh smoothing method strives to improve the shape quality of all elements. Generally a mesh consisting of only well-shaped elements is desired in finite element analysis. Although a perfect-shaped element yields short computation time, even a well-shaped element, whose shape is close to a regular polygon, sometimes prolongs the computation time of solving the system of equations derived with the edge-based finite element method. In this paper, we propose a new smoothing scheme of improving a convergence property of the system of equations by applying a common mesh smoothing method to some elements, which cause long computation time of the iterative solver. The proposed smoothing scheme utilizes the condition number of submatrices, into which coefficient matrix derived with the edge-based finite element method is subdivided, in order to choose ill-conditioned elements to be smoothed. As a result, the computation time is shortened applying a smoothing process only to the chosen ill-conditioned elements. [ABSTRACT FROM AUTHOR]

Abstract: State analysis of linear time-varying descriptor systems via hybrid functions are proposed in this paper. Based upon some useful properties of hybrid functions, a special product matrix and a related coefficient matrix are applied to solve the descriptor systems. The unknown coefficient matrix will be in generalized Lyapunov equation form, which is solved via the Kronecker product method. The advantages of hybrid functions are not only the values of n and m are adjustable but also it can yield more accurate numerical solutions than orthogonal functions and orthogonal polynomials to the problems of solving the descriptor systems. We propose that the available optimal values of n and m can minimize the relative errors in the numerical solutions. The high accuracy and the wide applicability of hybrid function approach will be demonstrated with numerical examples. [Copyright &y& Elsevier]

In this paper, an improved procedure for imposing displacement boundary conditions in the direct stiffness method of the finite element analysis is presented. The proposed procedure neither changes the original order of the master stiffness matrix, nor does it require the rearrangement of the coefficient matrix. Consequently, it is easy to be implemented. Especially, the condition numbers of coefficient matrices of the improved procedure are remarkably reduced; hence the sensitivity of the solution to perturbations is considerably lowered. Numerical examples are used to demonstrate the validity of the proposed procedure. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]