Search

In this paper, we consider the aeroelastic flutter problem (AEFP) in terms of matrix equations. We provide a general framework on the spectral theory of three parameter AEFP in tensor product space under the auspices of the techniques of multiparameter eigenvalue problems (MEP) in matrix form. It is to noted that, the AEFP of an undamped system can be converted to a linear singular two parameter eigenvalue problem (2PEP) in double dimension and by quasilinearization technique it can be converted to a linear three parameter eigenvalue problem (3PEP) of the same dimension. The de-facto way to find the numeric of MEP is by solving associated joint generalised eigenvalue problem (GEP) using conventional numerical method, provided the problem being nonsingular. Since the transformed version of AEFP in matrix form is singular, so the usual solution techniques for MEP can not be applied to address AEFP and it necessitates to adopt alternate numerical techniques for the same. In the current paper, it is intended to address singular AEFP under certain assumptions. The paper also serves as a report on the Kronecker product method, so called Delta method developed by Atkinson for finding finite eigenvalues of singular three parameter AEFP. [ABSTRACT FROM AUTHOR]

In this paper, the power method is discussed in mathematical detail with respect to the convergence, analysis, numerical computations and multiplicity. Deflation as well as avoiding deflation are described for symmetric positive definite matrices. Variations of the power method are discussed. Projections are applied to some distributions of the spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we advocate a new technique to determine inner bounds for the extreme eigenvalues of real symmetric matrices. Our method involves the matrix elements and compares favourably with existing methods. We also show how the bounds can be optimized. [ABSTRACT FROM AUTHOR]

This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]

In this paper, we show how the outer bounds of the extremal eigenvalues of real positive definite symmetric irreducible matrices may be improved by the simple application of optimizing the Gerschgorin bounds. The method is easy to apply and yields fairly accurate results with minimal effort. [ABSTRACT FROM AUTHOR]

This paper is concerned with discrete secondorder coupled boundary value problems with sign-changing weight. We find that these problems have T real eigenvalues (including the multiplicity). Specifically, the numbers of positive eigenvalues are equal to the number of positive elements in the weight function, and the numbers of negative eigenvalues are equal to the number of negative elements in the weight function. Furthermore, the relationships between the eigenvalues under three different coupled boundary conditions are established. These results extend the relevant existing results of periodic and anti-periodic boundary value problems with sign-changing weight and the coupled boundary value problems with definite weight. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the onedimensional perturbation L = H+V, where H is the harmonic oscillator and V is a decreasing scalar potential. It is well known that the eigenvalues of L can be expressed as 2k + 1 + μk. The main result of the paper is to describe an asymptotic formula for the fluctuation {μk} when k tends to infinity. [ABSTRACT FROM AUTHOR]

The partial complement of a graph G with respect to a set S denoted by G⊕S is the graph obtained by removing the edges of 〈S〉 and adding edges which are not in 〈S〉 in G. In this paper we introduce the concept of Seidel energy of partial complement of a graph. Some bounds are obtained for Seidel energy of partial complementary graph. We compute Seidel energy and Seidel spectrum for partial complement of several classes of graph. [ABSTRACT FROM AUTHOR]

In this paper, some new estimations of diagonally dominant degree on the Schur complement of I(II)-block diagonally dominant matrices are obtained by applying the properties of Schur complement and some inequality techniques, which improve some existing ones. Further, as an application, we present some new distribution theorems for eigenvalues of the Schur complement and some new upper and lower bounds for the determinant of I(II)-block diagonally dominant matrices. These results are proved to be sharper than some known ones. Finally, numerical examples are also presented to confirm the theoretical results studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a fast range and bearing estimation method for a single near-field source is proposed. By constructing the covariance matrix of received data, the phase containing the information of range and the direction of arrival is extracted. Finally, the phase is rewritten as matrix form, and the closed-formed solution of range and bearing of the source can be calculated by least square method. In contrast to high-order statistics based methods, the proposed method can obtain the range and bearing estimation without eigenvalue decomposition and spectral search, which remarkably reduce computational complexity. Simulation results show the proposed method can provide improved estimation accuracy and higher efficiency. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to establish iterative algorithms for computing the Takagi factorization of complex symmetric matrices. Similar to the classical iterative algorithms of computing the eigenpairs of real symmetric matrices, we derive power-like iterations for computing the Takagi values and associated Takagi vectors of complex symmetric matrices, i.e., the power-like method, the orthogonal-like iteration and the complex symmetric QR-like iteration. We analyze the convergence of these algorithms under some mild conditions. We also investigate the Jacobi-like methods for computing the Takagi factorization of complex symmetric matrices like Jacobi's methods for real symmetric eigenvalue problems. We illustrate our algorithms via numerical examples. [ABSTRACT FROM AUTHOR]

The energy of G is defined as the sum of absolute value of all eigenvalues of the adjacency matrix A(G). Let B²(n, a, b, p) be the set of all bicyclic graphs on n vertices with p pendent vertices and two cycles Ca and Cb which have unique common vertex u0, Bθ²(n, a, b, p) the graph class obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sn-(a + b - 1)+1, and Bµ² (n, a, b, p) the set obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sp and connecting a pendent path Pn - (a + b -1)-(p - 1) on point u0. In this paper, it is obtained that Bθ² (n, a, b, p) has the minimal energy in all graphs which have only pendent vertices except two cycles, and Bµ² (n, a, b, p) has the minimal energy in all graphs which have prescribed cycles' length and pendent vertices. [ABSTRACT FROM AUTHOR]

Some new convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix and an inverse M-matrix are given. Numerical examples show that these bounds could reach the true value of the minimum eigenvalue in some cases. These bounds in this paper improve some existing ones. [ABSTRACT FROM AUTHOR]

In this paper, a Mackey-Glass equation with time-varying delay is investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some numerical simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies. [ABSTRACT FROM AUTHOR]

This paper develops a method for automatically incorporating variable selection in Fisher's linear discriminant analysis (LDA). Utilizing the connection of Fisher's LDA and a generalized eigenvalue problem, our approach applies the method of regularization to obtain sparse linear discriminant vectors, where "sparse" means that the discriminant vectors have only a small number of nonzero components. Our sparse LDA procedure is especially effective in the so-called high dimensional, low sample size (HDLSS) settings, where LDA possesses the "data piling" property, that is, it maps all points from the same class in the training data to a common point, and so when viewed along the LDA projection directions, the data are piled up. Data piling indicates overfitting and usually results in poor out-of-sample classification. By incorporating variable selection, the sparse LDA overcomes the data piling problem. The underlying assumption is that, among the large number of variables there are many irrelevant or redundant variables for the purpose of classification. By using only important or significant variables we essentially deal with a lower dimensional problem. Both synthetic and real data sets are used to illustrate the proposed method. [ABSTRACT FROM AUTHOR]