相关论文: Rational approximation preconditioners for multiph…

In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…

This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…

Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…

Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far…

Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on…

This paper deals with two main topics related to Diophantine approximation. Firstly, we show that if a point on an algebraic variety is approximable by rational vectors to a sufficiently large degree, the approximating vectors must lie in…

Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of…

In this paper the properties of R\'edei rational functions are used to derive rational approximations for square roots and both Newton and Pad\'e approximations are given as particular cases. As a consequence, such approximations can be…

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…

We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Pad\'e approximants are far more accurate than more elaborate…

This paper deals with the complex problem of how to simulate multiparticle contacts. The collision process is responsible for the transfer and dissipation of energy in granular media. A novel model of the interaction force between particles…

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…

The classical approximation may be applied to a number of problems in non-equilibrium field theory. The principles and limits of classical real-time lattice simulations are presented, with particular emphasis on the definition of particle…

We present preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from finite element discretizations of the fictitious domain method with Lagrange multipliers. In…

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…

In the finite difference approximation of the fractional Laplacian the stiffness matrix is typically dense and needs to be approximated numerically. The effect of the accuracy in approximating the stiffness matrix on the accuracy in the…

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…