Related papers: On node distributions for interpolation and spectr…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
Double parton distributions are the nonperturbative ingredients needed for computing double parton scattering processes in hadron-hadron collisions. They describe a variety of correlations between two partons in a hadron and depend on a…
In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
Chebyshev spectral methods are widely used in numerical computations. When the underlying function has a singularity, it has been observed by L. N. Trefethen in 2011 that its Chebyshev interpolants exhibit an error localization property,…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
In this paper we analyze the use of Chebyshev polynomials in distributed consensus applications. We study the properties of these polynomials to propose a distributed algorithm that reaches the consensus in a fast way. The algorithm is…
The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…
This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the…
In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can lead to highly inaccurate results due to numerical…
The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge…
We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…
Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
We present an algorithm for producing discrete distributions with a prescribed nearest-neighbor distance function. Our approach is a combination of quasi-Monte Carlo (Q-MC) methods and weighted Riesz energy minimization: the initial…
We present the simulation of the time evolution of the distance matrix. The result is the node-node distance distribution for various kinds of networks. For the exponential trees, analytical formulas are derived for the moments of the…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
In this work, a family of symmetric interpolation points are generated on the four-dimensional simplex (i.e. the pentatope). These points are optimized in order to minimize the Lebesgue constant. The process of generating these points…