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We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is…
We herein propose a variant of the projected inexact Levenberg--Marquardt method (ILMM) for solving constrained nonsmooth equations. Since the orthogonal projection onto the feasible set may be computationally expensive, we propose a local…
We describe a method for constructing $n$-orthogonal coordinate systems in constant curvature spaces. The construction proposed is a modification of Krichever's method for producing orthogonal curvilinear coordinate systems in the…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…
Octilinear graph drawings are a standard paradigm extending the orthogonal graph drawing style by two additional slopes (+1 and -1). We are interested in two constrained drawing problems where the input specifies a so-called representation,…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
Recently, novel quaternion-valued wavelets on the plane were constructed using an optimisation approach. These wavelets are compactly supported, smooth, orthonormal, non-separable and truly quaternionic. However, they have not been tested…
Methods which aim at universal applicability must be able to describe both weak and strong electronic correlation with equal facility. Such methods are in short supply. The combination of symmetry projection for strong correlation and…
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…