We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process efficiently and robustly compute coefficients of approximation. second is based an optimization formulation that allows us include structural constraints approxim...

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

We study infinitely repeated symmetric 2×2 games played by bounded rational agents who follow a simple rule of thumb: each agent continues to play the same action if the current payoff exceeds the average of the past payoffs, and switches to the other action with a positive probability otherwise. By applying the stochastic approximation technique, we characterize the asymptotic outcomes for all...

We study a constructive method of rational approximation of analytic functions based on ideas of the theory of Hankel operators. Some properties of the corresponding Hankel operator are investigated. We also consider questions related to the convergence of rational approximants. Analogues of Montessus de Ballore’s and Gonchars’s theorems on the convergence of rows of Padé approximants are proved.

In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We...

Let α(E) be the continuous analytic capacity of a compact set E ⊂ C. In this paper we obtain a characterization of α in terms of curvature of measures with zero linear density, and we deduce that α is countably semiadditive. This result has important consequences for the theory of uniform rational approximation on compact sets. In particular, it implies the so called inner boundary conjecture.