We discuss the design and development of a new Fortran code EA16 for the computation of selected eigenvalues and eigenvectors of large-scale real symmetric eigenvalue problems. EA16 can be used for either the standard or the generalized eigenvalue problem. The underlying method used by EA16 is the block Lanczos method with partial reorthogonalization plus implicit restarting, combined with purg...

This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a sligh...

This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a sligh...

This paper considers the problem of robust eigenstructure assignment, which involves finding a feedback gain matrix that makes the closed-loop system insensitive to perturbations or parameter variations. The main contribution of the paper is to derive a new robustness measure using the matrix perturbation theory. The new measure is used to formulate a new method for robust control of the system...

This paper presents CH-SAT, a Complete Heuris-tic procedure for the SATissability problem (SAT) based on local search techniques. CH-SAT aims to combine the ee-ciency of local search and the completeness of memorizing-backtracking. CH-SAT extends successively a consistent partial assignment using a complete assignment as guidance for variable-ordering. To extend the partial assignment, CH-SAT u...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly nonlinear water wave models, the physical system considered here is nonlinearly dispersive, and contains nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in presence of a large parameter. Combining the technique of singular perturbation...

In this paper, we propose the palindromic doubling algorithm (PDA) for the palindromic generalized eigenvalue problem (PGEP) A∗x = λAx. We establish a complete convergence theory of the PDA for PGEPs without unimodular eigenvalues, or with unimodular eigenvalues of partial multiplicities two (one or two for eigenvalue 1). Some important applications from the vibration analysis and the optimal c...

Let Ω be an open, simply connected, and bounded region in R, d ≥ 2, and assume its boundary ∂Ω is smooth. Consider solving the eigenvalue problem Lu = λu for an elliptic partial differential operator L over Ω with zero values for either Dirichlet or Neumann boundary conditions. We propose, analyze, and illustrate a ‘spectral method’ for solving numerically such an eigenvalue problem. This is an...