A rational spectral problem in fluid-solid vibration.
Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix.
Locating real eigenvalues of a spectral problem in fluid-solid type structures.
A fast algorithm for solving regularized total least squares problems.
A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration
In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.
Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
Rational Krylov for nonlinear eigenproblems, an iterative projection method
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably...
Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting
In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative...
Page 1