DeepAI AI Chat
Log In Sign Up

Multivariate Rational Approximation

12/03/2019
by   Anthony P. Austin, et al.
0

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 to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation, resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

READ FULL TEXT
09/22/2020

Multivariate Rational Approximation Using a Stabilized Sanathanan-Koerner Iteration

The Sanathanan-Koerner iteration developed in 1963 is classical approach...
08/20/2021

Flexible rational approximation for matrix functions

A rational approximation is a powerful method for estimating functions u...
03/08/2023

A comparison of rational and neural network based approximations

Rational and neural network based approximations are efficient tools in ...
06/06/2022

Sparse Bayesian Learning for Complex-Valued Rational Approximations

Surrogate models are used to alleviate the computational burden in engin...
01/22/2019

Support Estimation via Regularized and Weighted Chebyshev Approximations

We introduce a new framework for estimating the support size of an unkno...
03/16/2017

Ultimate Positivity of Diagonals of Quasi-rational Functions

The problem to decide whether a given multivariate (quasi-)rational func...
04/17/2020

A case study for ζ(4)

Using symbolic summation tools in the setting of difference rings, we pr...