On regression analysis with Pad\'e approximants

TL;DR

This paper explores the use of Padé approximants in two-dimensional regression analysis, proposing a new residual formulation, regularization techniques, and demonstrating practical applications in physics and reliability theory.

Contribution

Introduces a novel residual formulation for Padé approximants in regression, incorporating Tikhonov regularization to prevent overfitting, with practical case studies.

Findings

Effective in physics data fitting

Regularization reduces overfitting

System of linear equations simplifies computations

Abstract

The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using Tikhonov regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered.