Generalized Inverse Eigenvalue Problem for Centrohermitian Matrices

In this paper we first consider the existence and the general form of solution to the following generalized inverse eigenvalue problem(GIEP): given a set of n-dimension complex vectors {x j}m j=1 and a set of complex numbers {λ j}m j=1, find two n×n centrohermitian matrices A,B such that {x j}m j=1 and {λ j}m j=1 are the generalized eigenvectors and generalized eigenvalues of Ax=λBx, respectively. We then discuss the optimal approximation problem for the GIEP. More concretely, given two arbitrary matrices, , ∈C n×n, we find two matrices A and B such that the matrix (A*,B*) is closest to (,) in the Frobenius norm, where the matrix (A*,B*) is the solution to the GIEP. We show that the expression of the solution of the optimal approximation is unique and derive the expression for it.

A direct-variance-analysis method for generalized stochastic eigenvalue problem based on matrix perturbation theory

It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.

Stability analysis of discrete-time BAM neural networks based on standard neural network models

To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.

Generalized Inverse Eigenvalue Problem for (P,Q)-Conjugate Matrices and the Associated Approximation Problem

In this paper,the generalized inverse eigenvalue problem for the（P,Q）-conjugate matrices and the associated approximation problem are discussed by using generalized singular value decomposition（GSVD）.Moreover,the least residual problem of the above generalized inverse eigenvalue problem is studied by using the canonical correlation decomposition（CCD）.The solutions to these problems are derived.Some numerical examples are given to illustrate the main results.

The Magnetic Field as Trigger for Disturbances of a Flow of a Newtonian Fluid through a Cylindrical Pipe with a Horizontal Axis

A Fourrier Petrov Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables. It is written in FORTRAN. Systematic studies are presented on the dependence of eigenvalues and other quantities on the axial and azimuthal wave number;the reynolds’ number Re and a new none-dimensional number Ne. The flow will be considered stable if all the real parts of the eigenvalues are negative and unstable if only one of them is positive.