Related papers: A stable, polynomial-time algorithm for the eigenp…
In this paper, we present a protocol for computing the principal eigenvector of a collection of data matrices belonging to multiple semi-honest parties with privacy constraints. Our proposed protocol is based on secure multi-party…
We introduce the problem of adapting a stable matching to forced and forbidden pairs. Specifically, given a stable matching $M_1$, a set $Q$ of forced pairs, and a set $P$ of forbidden pairs, we want to find a stable matching that includes…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in…
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…
This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations.…
The purpose of this paper is to show how the problem of finding the zeros of unilateral n-order quaternionic polynomials can be solved by determining the eigen-vectors of the corresponding companion matrix. This approach, probably…
We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…
We study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n-dimensional quaternionic vector spaces. For quaternionic linear operators the eigenvalue spectrum consists of n complex values. For…
In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…
Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework…
We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to…
In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including the semiring of nonnegative real numbers and all idempotent…
This paper continues research initiated in quant-ph/0201022 . The main subject here is the so-called Edmonds' problem of deciding if a given linear subspace of square matrices contains a nonsingular matrix . We present a deterministic…
The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = \lambda x$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $\lambda $ refers to maximum…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
Various physical models can be expressed in terms of matrices. A valuable tool for analysing matrix models is numerical simulations, often the Metropolis algorithm with various improvements. The downside of this approach is that the…
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…
We establish the first globally convergent algorithms for computing the Kreiss constant of a matrix to arbitrary accuracy. We propose three different iterations for continuous-time Kreiss constants and analogues for discrete-time Kreiss…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…