Related papers: Iterative Polynomial Approximation Algorithms for …
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…
Previous works show convergence of rational Chebyshev approximants to the Pad\'e approximant as the underlying domain of approximation shrinks to the origin. In the present work, the asymptotic error and interpolation properties of rational…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…
This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an…
In this paper we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional first and second kind Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality…
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by…
We investigate deep composite polynomial approximations of continuous but non-differentiable functions with algebraic cusp singularities. The functions in focus consist of finitely many cusp terms of the form $|x-a_j|^{\alpha_j}$ with…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…
Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized…
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…