The total least squares (TLS) method is a successful approach for linear problems if both the system matrix and the right hand side are contaminated by some noise. For ill-posed TLS problems Renaut and Guo [SIAM J. Matrix Anal. Appl., 26 (2005), pp. 457 476] suggested an iterative method which is based on a sequence of linear eigenvalue problems. Here we analyze this method carefully, and we ac...

a method for solving the descriptor discrete-time linear system is focused. for easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. in partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

Solving (nonlinear) eigenvalue problems by contour integration, requires an e↵ective discretization for the corresponding contour integrals. In this paper it is shown that good rational filter functions can be computed using (nonlinear least squares) optimization techniques as opposed to designing those functions based on a thorough understanding of complex analysis. The conditions that such an...

We obtain the asymptotics, as $t + |x| \rightarrow \infty$, of fundamental solution to heat equation with a compactly supported potential. It is assumed that corresponding stationary operator has at least one positive eigenvalue. Two regions different types behavior are distinguished: inside certain conical surface in $(t,x)$ space, asymptotics determined by principal eigenvalue and eigenfuncti...

The set S(g, n) of all stochastic matrices of order n whose directed graph has girth g is considered. For any g and n, a lower bound is provided on the modulus of a subdominant eigenvalue of such a matrix in terms of g and n, and for the cases g = 1, 2, 3 the minimum possible modulus of a subdominant eigenvalue for a matrix in S(g, n) is computed. A class of examples for the case g = 4 is inves...

In this paper we consider the transmission eigenvalue problem corresponding to the scattering problem for an anisotropic magnetic materials with voids, i.e. subregions with refractive index the same as the background. Here we restrict ourselves to the scalar case of TE-polarization. Under weak assumptions on the material properties, we show that the transmission eigenvalues can be determined fr...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

The basic least squares method for identifying linear systems has been extensively studied. Conditions for convergence involve issues about noise assumptions and behavior of the sample covariance matrix of the regressors. Lai and Wei proved in 1982 convergence for essentially minimal conditions on the regression matrix: All eigenvalues must tend to in nity, and the logarithm of the largest eige...

We propose two semismooth Newton methods for seeking the eigenvalues of a linear transformation relative to Lorentz cones, by the natural equation reformulation and the normal equation reformulation, respectively, and establish their local quadratic convergence results under suitable conditions. The convergence analysis shows that the method based on the natural equation formulation is not infl...