Related papers: A stable, polynomial-time algorithm for the eigenp…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…
Quadratic eigenvalue problems (QEP) and more generally polynomial eigenvalue problems (PEP) are among the most common types of nonlinear eigenvalue problems. Both problems, especially the QEP, have extensive applications. A typical approach…
We show that the two problems of computing the permanent of an $n\times n$ matrix of $\operatorname{poly}(n)$-bit integers and counting the number of Hamiltonian cycles in a directed $n$-vertex multigraph with…
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
This paper is a continuation of \ct{cmf16} where an efficient algorithm for computing the maximal eigenpair was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements.…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed rank their Ehrhart polynomials are computable in polynomial…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We consider the stable matching problem when the preference lists are not given explicitly but are represented in a succinct way and ask whether the problem becomes computationally easier and investigate other implications. We give…
The theory of eigenvalues and eigenvectors is one of the fundamental and essential components in tensor analysis. Computing the dominant eigenpair of an essentially nonnegative tensor is an important topic in tensor computation because of…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…