The residual inverse iteration is a simple method for solving eigenvalue problems that are nonlinear in the eigenvalue parameter. In this paper, we establish a new expression and a simple bound for the asymptotic convergence factor of this iteration in the special case that the nonlinear eigenvalue problem is Hermitian and admits a so called Rayleigh functional. These results are then applied t...

In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0, 2], and the real part is zero (respectively two) if and only if the eigenvalue is zero (respectively two). All the H+-eigenvalues of the Laplacian and all the smallest H+-eigenvalues of its sub-t...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

In this paper, the first and second order approximations of Taylor expansion are used for calculating the change of each natural frequency by modifying an arbitrary parameter of a system with a known amount and based on this approximation, the inverse eigenvalue problem is transformed to a solvable algebraic equation. The finite element formulation, based on the classical laminated plate theory...

We introduce a cross eigenvalue condition matrix for measuring the sensitivity of eigenvalue computations. A fundamental difference between this new object and traditional eigenvalue condition numbers is that cross interactions between eigenvectors that are not associated with the same eigenvalue are taken into account. We develop an abstract formulation that makes it possible to define continu...

A complete characterization of the convergence factor can be very useful when analyzing the asymptotic convergence of an iterative method. We will here establish a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well known inverse iteration. The formula for the convergence factor ...

The ‘monodromy conjecture’ for a hypersurface singularity f predicts that a pole of its topological (or related) zeta function induces one of its monodromy eigenvalues. However, in general only a few eigenvalues are obtained this way. The second author proposed to consider zeta functions associated with the hypersurface and with a differential form and raised the following question. Can one fin...

the stability analysis of islanded inverter-based microgrids (ibmgs) is increasingly an important and challenging topic due to the nonlinearity of ibmgs. in this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. using the linear model makes it easy to analyze the eigenvalues and stability of ibmgs due to the fact that it derive...

In this paper, only simple graphs are considered. A graphG is nonsingular if its adjacency matrix A(G) is nonsingular. A nonsingular graph G satisfies reciprocal eigenvalue property (property R) if the reciprocal of each eigenvalue of the adjacency matrix A(G) is also an eigenvalue of A(G) and G satisfies strong reciprocal eigenvalue property (property SR) if the reciprocal of each eigenvalue o...