Learn More
Many applications give rise to nonlinear eigenvalue problems with an underlying structured matrix polynomial. In this paper several useful classes of structured polynomial (e.g., palindromic, even, odd) are identified and the relationships between them explored. A special class of linearizations that reflect the structure of these polynomials, and therefore(More)
This paper extends the singular value decomposition to a path of matrices E(t). An analytic singular value decomposition of a path of matrices E(t) is an analytic path of factorizations E(t) = X(t)S(t)Y (t) T where X(t) and Y (t) are orthogonal and S(t) is diagonal. To maintain diierentiability the diagonal entries of S(t) are allowed to be either positive(More)
We study large, sparse generalized eigenvalue problems for matrix pencils, where one of the matrices is Hamiltonian and the other skew Hamiltonian. Problems of this form arise in the numerical simulation of elastic deformation of anisotropic materials, in structural mechanics and in the linear-quadratic control problem for partial diierential equations. We(More)
We discuss the state of the art in numerical solution methods for large scale polynomial or rational eigenvalue problems. We present the currently available solution methods such as the Jacobi-Davidson, Arnoldi or the rational Krylov method and analyze their properties. We briefly introduce a new linearization technique and demonstrate how it can be used to(More)
We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed specifically to have particular properties. A classification is given of polynomial eigenvalue problems according to their structural properties. Identifiers based on(More)
Palindromic polynomial eigenvalue problems and related classes of structured eigenvalue problems are considered. These structures generalize the concepts of symplectic and Hamiltonian matrices to matrix polynomials. We discuss several applications where these matrix polynomials arise, and show how linearizations can be derived that reflect the structure of(More)
This article describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given(More)
We discuss the eigenvalue problem for general and structured matrix polynomials which may be singular and may have eigenvalues at infinity. We derive condensed forms that allow (partial) deflation of the infinite eigenvalue and singular structure of the matrix polynomial. The remaining reduced order staircase form leads to new types of lineariza-tions which(More)
In this paper we give a survey on balanced truncation model order reduction for linear time-invariant continuous-time systems in descriptor form. We first give a brief overview of the basic concepts from linear system theory and then present balanced truncation model reduction methods for descriptor systems and discuss their algorithmic aspects. The(More)