Related papers: Right-left asymmetry of the eigenvector method: A …
The article considers an inhomogeneous Erd\H{o}s-R\"enyi random graph on $\{1,\ldots, N\}$, where an edge is placed between vertices $i$ and $j$ with probability $\varepsilon_N f(i/N,j/N)$, for $i\le j$, the choice being made independent…
We study the inverse eigenvalue problem for finding doubly stochastic matrices with specified eigenvalues. By making use of a combination of Dykstra's algorithm and an alternating projection process onto a non-convex set, we derive hybrid…
Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely…
Complete and incomplete additive/multiplicative pairwise comparison matrices are applied in preference modelling, multi-attribute decision making and ranking. The equivalence of two well known methods is proved in this paper. The arithmetic…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…
This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then a real geometric…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…
We develop a method to calculate left-right eigenvector correlations of the product of $m$ independent $N\times N$ complex Ginibre matrices. For illustration, we present explicit analytical results for the vector overlap for a couple of…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Consistent approximations obtained by geometric means ($GM$) and the principal eigenvector ($EV$), turned out to be close enough for 1,000,000 not-so-inconsistent pairwise comparisons matrices. In this respect both methods are accurate…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
In this paper, some main eigenvalues and eigenvectors of the politics matrix are investigated. The number of upper-class families in a society is the number of eigenvalues which are very close to 1. An algorithm to identify all the…
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
We study the eigenvectors and eigenvalues of random matrices with iid entries. Let $N$ be a random matrix with iid entries which have symmetric distribution. For each unit eigenvector $\mathbf{v}$ of $N$ our main results provide a small…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accuracy, extracting an approximate eigenpair…