The inverse eigenvalue problem of constructing symmetric positive semidefinite matrixD written as D ≥ 0 and real-valued skew-symmetric matrix G i.e., G −G of order n for the quadratic pencilQ λ : λMa λ D G Ka, whereMa > 0,Ka ≥ 0 are given analytical mass and stiffness matrices, so that Q λ has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient condition...

The T-palindromic quadratic eigenvalue problem (λB + λC + A)x = 0, with A,B,C ∈ Cn×n, C = C and B = A, governs the vibration behavior of trains. One way to solve the problem is to apply a structure-preserving doubling algorithm (SDA) to the nonlinear matrix equation (NME) X + BX−1A = C and “square-root” the matrix quadratic involved. In this paper, we generalize the SDA for the solution of (odd...

This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadratically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative procedure for solving the regularized Total...

Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve eigenproblems. rIGA discretization, while conserving desirable properties maximum-continuity (IGA), reduces interconnection between degrees freedom by adding low-continuity basis functions. This connectivity reduction in rIGA’s alge...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...

The eigenvalues of a Hermitian matrix function that depends on one parameter analytically can be ordered so that each eigenvalue is an analytic function of the parameter. Ordering these analytic eigenvalues from the largest to the smallest yields continuous and piece-wise analytic functions. For multi-variate Hermitian matrix functions that depend on d parameters analytically, the ordered eigen...