Related papers: Arithmetic, interpolation and factorization of ama…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…
In this paper we show that the weighted Bernstein-Walsh inequality in logarithmic potential theory is sharp up to some new universal constant, provided that the external field is given by a logarithmic potential. Our main tool for such…
Generative models based on normalizing flows are very successful in modeling complex data distributions using simpler ones. However, straightforward linear interpolations show unexpected side effects, as interpolation paths lie outside the…
Variational interpolants are an indispensable tool for the construction of gradient-flow solutions via the Minimizing Movement Scheme. The De Giorgi lemma provides the associated discrete energy-dissipation inequality. It was originally…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
In contemporary deep learning practice, models are often trained to near zero loss i.e. to nearly interpolate the training data. However, the number of parameters in the model is usually far more than the number of data points n, the…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…
The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…
Let $\mathcal{A}$ be an affine hyperplane arrangement, $L(\mathcal{A})$ its intersection poset, and $\chi_{\mathcal{A}}(t)$ its characteristic polynomial. This paper aims to propose combinatorial structures for the factorization of…
Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
We recognise that an entropy inequality akin to the main intermediate goal of recent works (Gowers, Green, Manners, Tao [3],[2]) regarding a conjecture of Marton provides a black box from which we can also through a short deduction recover…
Stopping-time Banach spaces is a collective term for the class of spaces of eventually null integrable processes that are defined in terms of the behaviour of the stopping times with respect to some fixed filtration. From the point of view…
We present a novel barycentric interpolation algorithm designed for analytic functions $f\in\mathcal{A}(E)$ defined on the complex plane. The algorithm, which encompasses both polynomial and rational interpolation, is tailored to handle…
The Peetre "plus-minus" interpolation spaces $\left\langle A_{0},A_{1}\right\rangle _{\theta}$ are defined variously via conditions about the unconditional convergence of certain Banach space valued series whose terms have coefficients…