Abstract
Eigenvalue problems involving large, sparse matrices with Hamiltonian or related structure arise in numerous applications. Hamiltonian problems can be transformed to symplectic or skew-Hamiltonian problems and then solved. This chapter focuses on the transformation to skew-Hamiltonian form and solution by the SHIRA method. Related to, but more general than, Hamiltonian matrices are alternating and palindromic pencils. A SHIRA-like method that operates on alternating (even) pencils M-λN and can be used even when N is singular, is presented.
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CITATION STYLE
Watkins, D. S. (2015). Large-scale structured eigenvalue problems. In Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory: Festschrift in Honor of Volker Mehrmann (pp. 25–43). Springer International Publishing. https://doi.org/10.1007/978-3-319-15260-8_2
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