The convergence analysis of iterative methods for nonlinear eigenvalue problems is in the most cases restricted either to algebraic simple eigenvalues or to polynomial eigenvalue problems. In this paper we consider two classical methods for general holomorphic eigenvalue problems, namely the nonlinear generalized Rayleigh quotient iteration (NGRQI) and the augmented Newton method. For both meth...

in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

The eigenvalues of the kernel matrix play an important role in a number of kernel methods, in particular, in kernel principal component analysis. It is well known that the eigenvalues of the kernel matrix converge as the number of samples tends to infinity. We derive probabilistic finite sample size bounds on the approximation error of individual eigenvalues which have the important property th...

In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite element analysis. Bounds are derived for the eigenvalues and the condition numbers, which are valid for stiffness matrices based on a set of general basis functions that can be used in the p-version. For a set of hierarchi...

We perform high-order sensitivity analysis of eigenvalues of linear systems depending on parameters. Attention is focused on double not-semi-simimple and semi-simple eigenvalues, undergoing perturbations, either of regular or singular type. The use of integer (Taylor) or fractional (Puiseux) series expansions is discussed, and the analysis carried out on the characteristic polynomial. It is sho...

Nowadays, analytical instruments that produce a data matrix for one chemical sample enjoy a widespread popularity. However, for a successful analysis of these data an accurate estimate of the pseudorank of the matrix is often a crucial prerequisite. A large number of methods for estimating the pseudorank are based on the eigenvalues obtained from principal component analysis (PCA) . In this pap...