Minimal state-space realization in linear system theory: an overview
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Matrix algorithms
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Numerical simulation of three dimensional pyramid quantum dot
Journal of Computational Physics
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Algorithm 849: A concise sparse Cholesky factorization package
ACM Transactions on Mathematical Software (TOMS)
Iterative projection methods for computing relevant energy states of a quantum dot
Journal of Computational Physics
The Conditioning of Linearizations of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
SIAM Journal on Matrix Analysis and Applications
Vector Spaces of Linearizations for Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Symmetric Linearizations for Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
NLEVP: A Collection of Nonlinear Eigenvalue Problems
ACM Transactions on Mathematical Software (TOMS)
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The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and properties of the original rational eigenvalue problem. For example, the low-rank property leads to a trimmed linearization. We show that solving a class of rational eigenvalue problems is just as convenient and efficient as solving linear eigenvalue problems.