Related papers: Norm Convergence of Realistic Projection and Refle…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averaged projections, cyclic products, quasi-periodic products and…
This paper derives bounds for the ratio of residual norms in the refined and Rayleigh- Ritz projection methods. To do this, it uses the Least squares and line search projection method proposed in [6]. The bound derived in this paper is less…
The article addresses the problem of image sampling with minimal possible sampling rates and reviews the recent advances in sampling theory and methods: modern formulations of the sampling theorems, potentials and limitations of Compressed…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
In this paper we explore the possibility of using computational algebraic methods to analyze a class of consensus protocols. We state some necessary conditions for convergence under consensus protocols that are polynomials.
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
Take a multidimensional normally or obliquely reflected diffusion in a smooth domain. Approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…
Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather "simpler" statistical model, which, in turn, results…
Projection mapping seamlessly merges real and virtual worlds. Although much effort was made to improve its image qualities so far, projection mapping is still unnatural. We introduce the first steps towards natural projection mapping by…