An interval-matrix branch-and-bound algorithm for bounding eigenvalues

An interval-matrix branch-and-bound algorithm for bounding eigenvalues

We present and explore the behaviour of a branch-and-bound algorithm for calculating valid bounds on the k-th largest eigenvalue of a symmetric interval matrix. Branching on the interval elements of the matrix takes place in conjunction with the application of Rohn’s method (an interval extension of Weyl’s theorem) in order to obtain valid outer bounds on the eigenvalues. Inner bounds are obtai...

An Interval Branch and Bound Algorithm for Parameter Estimation

The parameter estimation problem is a widespread and challenging problem in engineering sciences consisting in computing the parameters of a parametric model that fit observed data. The computer vision community has proposed the RANSAC algorithm to deal with outliers in the observed data. This randomized algorithm is efficient but non-deterministic and therefore incomplete. Jaulin et al. propos...

An interval branch and bound algorithm for bound constrained optimization problems

In this paper, we propose modiications to a prototypical branch and bound algorithm for nonlinear optimization so that the algorithm eeciently handles constrained problems with constant bound constraints. The modiications involve treating subregions of the boundary identically to interior regions during the branch and bound process, but using reduced gradients for the interval Newton method. Th...

A branch and bound algorithm for the matrix bandwidth minimization

In this article we first review previous exact approaches as well as theoretical contributions for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This NP-complete problem can also be formulated as a labeling o...

Gauss elimination algorithm for interval matrix