We compare various algorithms for constructing a matrix of order n whose Pareto spectrum contains a prescribed set Λ = {λ1, . . . , λp} of reals. In order to avoid overdetermination one assumes that p does not exceed n2. The inverse Pareto eigenvalue problem under consideration is formulated as an underdetermined system of nonlinear equations. We also address the issue of computing Lorentz spec...

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

This paper studies a general inverse eigenvalue problem which generalizes many well-studied pole placement and matrix extension problems. It is shown that the problem corresponds geometrically to a so-called central projection from some projective variety. The degree of this variety represents the number of solutions the inverse problem has in the critical dimension. We are able to compute this...

In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices [Knyazev and Neymeyr, (2009)] is extended to the case of operators. We show that convergence is retained up to any tolerance if one only uses approximate ap...

An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behavior. Spectral information is entailed because the dynamical behavior often is governed by the underlying natur...

n this paper we present two fast numerical methods for computing the QR factorization of a Cauchy-like matrix C with data points lying on the real axis or on the unit circle in the complex plane. It is shown that the rows of the Q-factor of C give the eigenvectors of a rank structured matrix partially determined by some prescribed spectral data. This property establishes a basic connection betw...

A novel procedure for explicit construction of the entries of real symmetric matrices with assigned spectrum and the entries of the corresponding orthogonal modal matrices is presented. The inverse eigenvalue problem of symmetric matrices with some specific sign patterns including hyperdominant one is explicitly solved too. It has been shown to arise thereof a possibility of straightforward sol...

Introduction and Basic Concepts.- Regularization Theory for Equations of the First Kind.- by Discretization.- Inverse Eigenvalue Problems.- An Problem in Electrical Impedance Tomography.- Scattering Problem.- References.- Index

We propose an algorithm for solving the inverse eigenvalue problem for real symmetric block Toeplitz matrices with symmetric Toeplitz blocks. It is based upon an algorithm which has been used before by others to solve the inverse eigenvalue problem for general real symmetric matrices and also for Toeplitz matrices. First we expose the structure of the eigenvectors of the so-called generalized c...