Large-Scale Structured Eigenvalue Problems

David S. Watkins ()
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David S. Watkins: Washington State University, Department of Mathematics

Chapter Chapter 2 in Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, 2015, pp 25-43 from Springer

Abstract: 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 −λ N and can be used even when N is singular, is presented.

Keywords: Hamiltonian Eigenvalue Problem; skew-Hamiltonian Matrices; Arnoldi Process; Krylov Subspace Methods; Implicitly Restarted (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-15260-8_2

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DOI: 10.1007/978-3-319-15260-8_2

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