Results 41 to 50 of about 911 (185)

Degenerate Bernstein polynomials

Journal of Approximation Theory, 1983
For \(f\epsilon\) C[0,1], the n-th Bernstein polynomial \(B_ n(f;x)\) is a polynomial of exact degree n, although degeneracies can occur in some cases. For example, if f itself is a polynomial of degree m, then \(B_ n(f;x)\) is also of degree m for \(n\geq m\) (although not equal to f(x) except in the case \(m=1)\).
Freedman, David, Passow, Eli
openaire   +2 more sources

Detecting Relevant Deviations From the White Noise Assumption for Non‐Stationary Time Series

Journal of Time Series Analysis, EarlyView.
ABSTRACT We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non‐stationary time series. Second, we address the problem that a white noise test is usually not performed because one believes ...
Patrick Bastian
wiley   +1 more source

Empirical‐Process Limit Theory and Filter Approximation Bounds for Score‐Driven Time Series Models

Journal of Time Series Analysis, EarlyView.
ABSTRACT This article examines the filtering and approximation‐theoretic properties of score‐driven time series models. Under specific Lipschitz‐type and tail conditions, new results are derived, leading to maximal and deviation inequalities for the filtering approximation error using empirical process theory.
Enzo D'Innocenzo
wiley   +1 more source

A new family of q-Bernstein polynomials: probabilistic viewpoint

Arab Journal of Basic and Applied Sciences
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming [Formula: see text] is a random variable satisfying moment conditions, we use the generating function of ...
Ayse Karagenc, Mehmet Acikgoz, Serkan Araci   +2 more
doaj   +1 more source

Convergence properties of dynamic mode decomposition for analytic interval maps

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 179-206, February 2026.
Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji, Julia Slipantschuk, Oscar F. Bandtlow, Wolfram Just   +3 more
wiley   +1 more source

Variation Convergence for Bernstein Polynomials [PDF]

Proceedings of the American Mathematical Society, 1968
Abstract not ...
openaire   +1 more source

Bernstein Operators for Exponential Polynomials [PDF]

Constructive Approximation, 2008
Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $λ_{0},...,λ_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex conjugation. If the length of the interval $[ a,b] $ is smaller than $π/M_{n}$, where $M_{n}:=\max \left\{| \text{Im}% λ_{j}| :j=0,...,n ...
Aldaz, J. M., Kounchev, Ognyan, Render, Hermann   +2 more
openaire   +7 more sources

Fractional Novel Analytical Method (FNAM): An Improved Innovative Numerical Scheme to Solve Fractional Differential‐Difference Equations

Engineering Reports, Volume 8, Issue 2, February 2026.
This paper introduces the Fractional Novel Analytical Method (FNAM), a Taylor‐series‐based technique for approximating nonlinear fractional differential‐difference equations. Built on the Caputo derivative, FNAM achieves rapid convergence without relying on Adomian polynomials, perturbation schemes, or transform methods.
Uroosa Arshad, Mariam Sultana, Homan Emadifar, Atul Kumar   +3 more
wiley   +1 more source

Consistency of Approximation of Bernstein Polynomial-Based Direct Methods for Optimal Control

Machines, 2022
Bernstein polynomial approximation of continuous function has a slower rate of convergence compared to other approximation methods. “The fact seems to have precluded any numerical application of Bernstein polynomials from having been made.
Venanzio Cichella, Isaac Kaminer, Claire Walton, Naira Hovakimyan, António Pascoal   +4 more
doaj   +1 more source

Robust estimation of a Markov chain transition matrix from multiple sample paths

Statistica Neerlandica, Volume 80, Issue 1, February 2026.
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and stationary distribution from observed sample paths is a core statistical challenge, particularly when multiple ...
Lasse Leskelä, Maximilien Dreveton
wiley   +1 more source