In this paper, we are concerned with the computation of a few eigenpairs with smallest eigenvalues in absolute value of quadratic eigenvalue problems. We first develop a semiorthogonal generalized Arnoldi method where the name comes from the application of a pseudo inner product in the construction of a generalized Arnoldi reduction [25] for a generalized eigenvalue problem. The method applies ...

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Padé Approximate Linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only n+ lm, which is generally substantially smaller than the dimension 2n of th...

The low-rank damping term appears commonly in quadratic eigenvalue problems arising from physical simulations. To exploit the low-rank damping property, we propose a Padé approximate linearization (PAL) algorithm. The advantage of the PAL algorithm is that the dimension of the resulting linear eigenvalue problem is only nC `m, which is generally substantially smaller than the dimension 2n of th...

Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems. In [Linear Algebra Appl., 351–352 (2002) 455], the distance to the nearest non-hyperbolic or non-elliptic quadratic eigenvalue problem is obtained using a global minimization problem. This paper proposes explicit formulas to compute these distances and the optimal perturbations. The problem ...

In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the (S + S−1)-transform and Patel’s algorithm, the structurepreserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for...

QUADRATIC INVERSE EIGENVALUE PROBLEMS: THEORY, METHODS, AND APPLICATIONS Vadim Olegovich Sokolov, Ph.D. Department of Mathematical Sciences Northern Illinois University, 2008 Biswa Nath Datta, Director This dissertation is devoted to the study of quadratic inverse eigenvalue problems from theoretical, computational and applications points of view. Special attention is given to two important pra...

The numerical computation of derivatives of eigenvalues and eigenvectors has been an active research topic due to its wide applications in engineering and the physical sciences. There are many numerical methods available in the literatures for computing derivatives of eigenvalues and eigenvectors for standard eigenvalue problems and quadratic eigenvalue problems. However, almost all existing me...

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semideenite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoo between bound quality and computational eeort.