Related papers: On regression analysis with Pad\'e approximants
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
Pad\'e approximants are rational functions whose series expansion match a given series as far as possible. These approximants are usually written under a rational form. In this paper, we will show how to write them also under two different…
The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Pad\'e polynomials over the Pad\'e approximation procedure. The first part of the paper is devoted to…
Based on the mathematically well defined Pad\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
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…
Power series representations for special functions are computationally satisfactory only in the vicinity of the expansion point. Thus, it is an obvious idea to use instead Pad\'{e} approximants or other rational functions constructed from…
Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…
A representation of the Pad\'e approximation of the $Z$-transform of a signal as a resolvent of a tridiagonal matrix $J$ is given. Several formulas for the poles, zeros and residues of the Pad\'e approximation in terms of the matrix $J$ are…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
We present a novel method for calculating Pad\'e approximants that is capable of eliminating spurious poles placed at the point of development and of identifying and eliminating spurious poles created by precision limitations and/or noisy…
In this paper, we obtain the analytical solutions of two kinds of transcendental equations with numerous applications in college physics by means of Lagrange inversion theorem, and rewrite them in the form of ratio of rational polynomials…
Methods of Pad\'e approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spectral theory Stieltjes transform (Markov function) of…
The main purpose of this paper is to compare the convergence properties of Pad\'e approximants and rational Hermite-Pad\'e approximants for some model class of multivalued analytic functions based of the inverse Zhoukovsky transform. We…
We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates…