Related papers: Rational approximation preconditioners for multiph…
Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Pad\'e approximants to meromorphic functions. However, only recently this…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
The natural kinship between classical theories of interpolation and approximation is well explored. In contrast to this, the interrelation between interpolation and approximation is subtle and this duality is relatively obscure in the…
In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is…
This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the…
Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid compartments. We introduce a new numerical formulation and a…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
We derive parameter-robust quasi-optimal error estimates for mixed finite element methods for the nonlinear Darcy--Forchheimer equations with mixed boundary conditions. Using the framework of operator preconditioning, we also design…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…