M/G/1-type processes are commonly encountered when modeling modern complex computer and communication systems. In this tutorial, we present a detailed survey of existing solution methods for M/G/1-type processes, focusing on the matrix-analytic methodology. From first principles and using simple examples, we derive the fundamental matrix-analytic results and lay out recent advances. Finally, we...

In this paper, a generalization of the level dependent Quasi-Birth-and-Death (QBD) chains is presented. We analyze nested level dependent QBD chains and provide the complete characterization of their fundamental matrices in terms of minimal non-negative solutions of a number of matrix quadratic equations. Our results provide mixed matrix-geometric solution for the stationary distribution of nes...

We present a study on the critical time step for the numerical integration based on the Runge-Kutta method of the monodromy matrix (the fundamental matrix solution) associated with a set of n rst-order linear ordinary diierential equations with periodic coeecients. By applying the Liapunov-Schmidt method, for any dimension n and systems which are perturbations of autonomous systems, we give an ...

We propose a method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views. This factorization is only possible when the image points are correctly scaled. The major technical contribution of this paper is a practical method for the recovery of these scalings, using only fundamental matric...

This paper describes initial work on a family of projective reconstruction techniques that extract projection matrices directly and linearly from matching tensors estimated from image data. The simplest methods use fundamental matrices and epipoles, alternative ones use trilinear tensors. All of the data is treated uniformly, and there is no reliance on ‘privileged’ images or tokens. The approa...

We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more su...

This work presents an automatic hybrid matching of central catadioptric and perspective images. It is based on the hybrid epipolar geometry. The goal is to obtain correspondences between an omnidirectional image and a conventional perspective image taken from different points of view. Mixing both kind of images has multiple applications, since an omnidirectional image captures many information ...

Two methods are given for the calculus of the fundamental matrix for the generalized linear differential equations on the Banach space of functions of bounded variation. The main result extends the Peano-Baker formula in this framework.

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give a purely algebro-geometric proof of the projective reconstruction theorem by Hartley and Schaffalitzky [HS09].

This paper describes a direct, self-contained method for planar image rectification of stereo pairs. The method is based solely on an examination of the Fundamental matrix, where an improved method is given for the derivation of two projective transformations that horizontally align all the epipolar projections. A novel approach is proposed to uniquely optimise each transform in order to minimi...