The quadratic inverse eigenvalue problem (QIEP) is to find the three matrices M,C, and K, given a set of numbers, closed under complex conjugations, such that these numbers become the eigenvalues of the quadratic pencil P (λ) = λM + λC + K. The affine inverse quadratic eigenvalue problem (AQIEP) is the QIEP with an additional constraint that the coefficient matrices belong to an affine family, ...

The convergence analysis of iterative methods for nonlinear eigenvalue problems is in the most cases restricted either to algebraic simple eigenvalues or to polynomial eigenvalue problems. In this paper we consider two classical methods for general holomorphic eigenvalue problems, namely the nonlinear generalized Rayleigh quotient iteration (NGRQI) and the augmented Newton method. For both meth...

Abstract In this work a procedure to compute the dispersion curves for one dimensional viscoelastic waveguides exploiting the finite element based global mass matrix and complex stiffness matrix is proposed. The global matrices of a finite length portion of the waveguide, the unit cell, are post-processed by enforcing Bloch-type boundary conditions along the wave propagation direction and next ...

This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and its curvature is provided by modal derivatives obtained by sensitivity analysis of the eigenvalue problem, or its static approximation, along the vibration mo...

In this paper, we propose a parametric solution to the partial eigenvalue assignment problem by state feedback control for non-symmetric quadratic pencil in multi-input case using orthogonality relations between eigenvectors. Our solution can be implemented with only a partial knowledge of the spectrum and the corresponding eigenvectors of non-symmetric quadratic pencil. We show that the number...

In this paper we will look at two results in which a special para-Hermitian matrix polynomial appears in linear quadratic systems theory. The first result constitutes the first step in a dissipativity check. The second result shows that dissipativity is equivalent to the solvability of the infinitehorizon linear quadratic optimal control problem and that its solutions are given by the behavior ...

The Quadratic Arnoldi algorithm is an Arnoldi algorithm for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the Second Order Arnoldi method (SOAR). In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices ...

Based on various matrix decompositions, we compare different techniques for solving the inverse quadratic eigenvalue problem, where n× n real symmetric matrices M , C and K are constructed so that the quadratic pencil Q(λ) = λM + λC + K yields good approximations for the given k eigenpairs. We discuss the case where M is positive definite for 1≤ k ≤ n, and a general solution to this problem for...

A matrix is said to have the Perron-Frobenius property (strong Perron-Frobenius property) if its spectral radius is an eigenvalue (a simple positive and strictly dominant eigenvalue) with a corresponding semipositive (positive) eigenvector. It is known that a matrix A with the Perron-Frobenius property can always be the limit of a sequence of matrices A(ε) with the strong Perron-Frobenius prope...

This paper introduces a new method for simultaneous estimation of lens distortion and multi-view geometry using only point correspondences. The new technique has significant advantages over the current state-of-the art in that it makes more effective use of correspondences arising from any number of views. Multi-view geometry in the presence of lens distortion can be expressed as a set of point...