Palindromic companion forms for matrix polynomials of odd degree
Journal of Computational and Applied Mathematics
Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm
SIAM Journal on Matrix Analysis and Applications
On a Nonlinear Matrix Equation Arising in Nano Research
SIAM Journal on Matrix Analysis and Applications
NLEVP: A Collection of Nonlinear Eigenvalue Problems
ACM Transactions on Mathematical Software (TOMS)
Numerical studies on structure-preserving algorithms for surface acoustic wave simulations
Journal of Computational and Applied Mathematics
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In this paper, based on Patel's algorithm (1993), we propose a structure-preserving algorithm for solving palindromic quadratic eigenvalue problems (QEPs). We also show the relationship between the structure-preserving algorithm and the URV-based structure-preserving algorithm by Schröder (2007). For large sparse palindromic QEPs, we develop a generalized $\top$-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi algorithm for solving the resulting $\top$-skew-Hamiltonian pencils. Numerical experiments show that our proposed structure-preserving algorithms perform well on the palindromic QEP arising from a finite element model of high-speed trains and rails.