Related papers: Comparing the Methods of Alternating and Simultane…

This technical note compares two coding (quantization) schemes for random projections in the context of sub-linear time approximate near neighbor search. The first scheme is based on uniform quantization while the second scheme utilizes a…

Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very…

We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equations can be accelerated to any given order of convergence by…

The method of cyclic projections finds nearest points in the intersection of finitely many affine subspaces. To accelerate convergence, Gearhart and Koshy proposed a modification which, in each iteration, performs an exact line search based…

Despite the success of a number of recent techniques for visual self-supervised deep learning, there has been limited investigation into the representations that are ultimately learned. By leveraging recent advances in the comparison of…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points…

This paper provides a duality gap convergence analysis for the standard ADMM as well as a linearized version of ADMM. It is shown that under appropriate conditions, both methods achieve linear convergence. However, the standard ADMM…

We study parallelisms on Veronese spaces associated with affine spaces, determine hyperplanes in Veronese spaces associated with projective spaces, and analyse the geometry of parallelisms determined by these hyperplanes.

Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…

We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension $N\geq 2$ and a lattice cone in a Hilbert space are considered.…

In this paper, we introduce a new method for classifying 3D objects. Our main idea is to project a 3D object onto a spherical domain centered around its barycenter and develop neural network to classify the spherical projection. We…

In this paper, some enhanced error estimates are derived for the augmented subspace methods which are designed for solving eigenvalue problems. We will show that the augmented subspace methods have the second order convergence rate which is…

We study the theoretical convergence of the nonlinear least-squares splitting method for the Monge-Amp\`ere equation in which each iteration decouples the pointwise nonlinearity from the differential operator and consists of a local…

In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal…

The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…

This work presents a systematic investigation into how alternative LiDAR-to-image projections affect metric place recognition when coupled with a state-of-the-art vision foundation model. We introduce a modular retrieval pipeline that…

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric.…

We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric…

The purpose of this paper is to prove that every finite set of points that can be constructed in the Euclidean plane by using a compass and a ruler can also be constructed by using unitary match-sticks in a non-simultaneous way and…