Related papers: A new rational approximation algorithm via the emp…
The performance of numerical micromagnetic models is limited by the demagnetizing field computation, which typically accounts for the majority of the computation time. For magnetization dynamics simulations explicit evaluation methods are…
We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an…
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…
We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process…
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial $f$ over an arbitrary finite field of size $q$. We assume a priori bounds $D$ and $T$ are given on the degree and number of terms…
We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…
We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…