Algorithm 854: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices II
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In this paper we present a survey of various algorithms for computing matrix geometric means and derive new second-order optimization algorithms to compute the Karcher mean. These new algorithms are constructed using the standard definition of the Riemanni ...
Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this wor ...
This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix-valued function is computationally expensive. ...
We consider a class of nonlinear eigenvalue problems including equations such as −Δu(x) + q(x)u(x) + γ u(x)2 ξ(x)2 + u(x)2 u = λu(x) for x ∈ R , where γ > 0, q ∈ L∞(RN ) and ξ ∈ L2(RN ) are given and we are interested in eigenvalues λ ∈ R for which this eq ...
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Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalu ...
We consider matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. One of the most fundamental differences from the linear case is that distinct eigenvalues may have linearly dependent eigenvectors or even share the same eigenvector. Th ...
A generalized matrix product can be formally written as Lambda(sp)(p) Lambda(sp-1)(p-1) ... Lambda(s2)(2) Lambda(s1)(1) where s(i) is an element of {- 1,+ 1} and ( A(1), ..., A(p)) is a tuple of ( possibly rectangular) matrices of suitable dimensions. The ...
Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modele ...
We investigate the performance of the routines in LAPACK and the Successive Band Reduction (SBR) toolbox for the reduction of a dense matrix to tridiagonal form, a crucial preprocessing stage in the solution of the symmetric eigenvalue problem, on general- ...
In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward st ...
