The problem of finding all intersections between two surfaces has many applications in computational geometry and computer-aided geometric design. We propose an algorithm based on Newton’s method and subdivision for this problem. Our algorithm uses a test based on the Kantorovich theorem to prevent the divergence or slow convergence problems normally associated with using unsuitable starting po...

This paper is dedicated to the problem of isolating and validating zeros non-linear two point boundary value problems. We present a method for such purpose based on Newton-Kantorovich Theorem rigorously enclose isolated with Neumann conditions.

In this paper, we provide a new form of upper bound for the converse of Jensen’s inequality. Thereby, known estimations of the difference and ratio in Jensen’s inequality are essentially improved. As an application, we also obtain an improvement of Kantorovich inequality.

This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction presented in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder. Résumé. Dans la présente note nous décrivons brièvement la construction introduite dans [7] à propo...

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector ...

We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation regularization in the context of image denoising and cartoon-texture decomposition. We point out connections of this approach to several other recently proposed me...

The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control prblem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to th...

We suggest a new method of describing invariant measures on Markov compacta and path spaces of graphs, and thus of describing characters of some groups and traces of AF-algebras. The method relies on properties of filtrations associated with the graph and, in particular, on the notion of a standard filtration. The main tool is the so-called internal metric that we introduce on simplices of meas...