In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Iterative methods for solving large, sparse, symmetric eigenvalue problems often encounter convergence diiculties because of ill-conditioning. The Generalized Davidson method is a well known technique which uses eigenvalue preconditioning to surmount these diiculties. Preconditioning the eigenvalue problem entails more subtleties than for linear systems. In addition, the use of an accurate conv...

A caterpillar is a tree in which the removal of all pendant vertices makes it a path. Let d ≥ 3 and n ≥ 6 be given. Let Pd−1 be the path of d − 1 vertices and Sp be the star of p + 1 vertices. Let p = [p1, p2, ..., pd−1] such that p1 ≥ 1, p2 ≥ 1, ..., pd−1 ≥ 1. Let C (p) be the caterpillar obtained from the stars Sp1 , Sp2 , ..., Spd−1 and the path Pd−1 by identifying the root of Spi with the i...

We study the eigenvalues of the biharmonic operators and the buckling eigenvalue on complete, open Riemannian manifolds. We show that the first eigenvalue of the biharmonic operator on a complete, parabolic Riemannian manifold is zero. We give a generalization of the buckling eigenvalue and give applications to studying the stability of minimal Lagrangian submanifolds in Kähler manifolds. MSC 1...

We present two theoretical results for the linear response eigenvalue problem. The first result is a minimization principle for the sum of the smallest eigenvalues with the positive sign. The second result is Cauchy-like interlacing inequalities. Although the linear response eigenvalue problem is a nonsymmetric eigenvalue problem, these results mirror the well-known trace minimization principle...

Until now several studies of rotating structures like rings or shells have been done. To model such problems in a right way, geometrical nonlinearity has to be considered. Different methods can used, solve the corresponding eigenvalue problem. In this article focus will placed on finite element method. contrast flat elements curved ones cause some numerical inconveniences. They include tremendo...

In this paper, based on a domain decomposition method, we propose an efficient two-level preconditioned Helmholtz-Jacobi-Davidson (PHJD) method for solving the algebraic eigenvalue problem resulting from edge element approximation of Maxwell problem. order to eliminate components in orthogonal complement space eigenvalue, shall solve parallel system and Helmholtz projection together fine space....