Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

Matrix polynomial eigenproblems arise in many application areas, both directly and as
approximations for more general nonlinear eigenproblems. One of the most common …

The Arnoldi method for standard eigenvalue problems possesses several attractive
properties making it robust, reliable and efficient for many problems. The first result of this …

Many numerical approximations rely on a simple iteration, X j+ 1= f (X j), to generate a
sequence {Xj} of approximations to a certain target. A doubling algorithm is an idea to …

We present structure‐preserving numerical methods for the eigenvalue problem of complex
palindromic pencils. Such problems arise in control theory, as well as from palindromic …

In this paper, the matrix equation AX+ X* B= C is considered, where the matrices A and B
have sizes m× n and n× m, respectively, the size of the unknown X is n× m, and the operator …

The T-palindromic quadratic eigenvalue problem $(\lambda^ 2 B+\lambda C+ A) x= 0$, with
$ A, B, C\in\mathbb {C}^{n\times n} $, $ C^ T= C $ and $ B^ T= A $, governs the vibration …

This work covers the analysis and numerical solution of certain structured eigenvalue
problems. For square complex matrices A, M, N a generalized eigenvalue problem of the …

The standard way to solve polynomial eigenvalue problems P (λ) x= 0 is to convert the
matrix polynomial P (λ) into a matrix pencil that preserves its spectral information—a process …