given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

Friedman has proposed a regularization technique RDA of discriminant anal ysis in the Gaussian framework RDA makes use of two regularization parameters to design an intermediate classi cation rule between linear and quadratic discriminant analysis In this paper we propose an alternative approach to design classi cation rules which have also a median position between linear and quadratic discrim...

The stability of non-diagonalizable networks of dynamical systems are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the synchronization state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable region of the modified system and specifying the eigenvalue distribution of the co...

We propose a Jacobi–Davidson type technique to compute selected eigenpairs of the product eigenvalue problem Am · · ·A1x = λx, where the matrices may be large and sparse. To avoid difficulties caused by a high condition number of the product matrix, we split up the action of the product matrix and work with several search spaces. We generalize the Jacobi–Davidson correction equation, and the ha...

The Automated Multi-Level Sub-structuring (AMLS) method is a powerful technique to determine a large number of eigenpairs with moderate accuracy of huge symmetric and definite eigenvalue problems in structural analysis. This paper is concerned with an adapted version of AMLS for eigenfrequency analysis of fluid-solid interaction systems. Although fluid-solid vibrations are governed by an unsymm...

This paper reviews numerical methods and analysis procedures used in the study of automotive disc brake squeal. It covers two major approaches used in the automotive industry, the complex eigenvalue analysis and the transient analysis. The advantages and limitations of each approach are examined. This review can help analysts to choose right methods and make decisions on new areas of method dev...

Based on the scalar Helmholtz equation and the finite-difference approximation, we formulate a matrix eigenvalue problem for the calculation of propagation constants, β(ω), in micro-structured optical fibres. The method is applied to index-guiding fibres as well as air-core photonic bandgap fibres, and in both cases qualitatively correct results are found. The strength of this approach lies in ...

We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider ẋα(t) = (G+α(t)F )xα(t), where G and F are 3×3 matrices with some prescribed structure. In the case of constant control α(t) ≡ α, we show the existence of an optimal Perron eigenvalue with respect to varying α under some a...

Omega3P is a parallel eigenmode calculation code for accelerator cavities in frequency domain analysis using finite-element methods. In this report, we will present detailed finite-element formulations and resulting eigenvalue problems for lossless cavities, cavities with lossy materials, cavities with imperfectly conducting surfaces, and cavities with waveguide coupling. We will discuss the pa...