Stochastic Bernstein polynomials: uniform convergence in probability with ratesSpringer Science and Business Media LLC - Tập 46 - Trang 1-10 - 2020
José A. Adell, Daniel Cárdenas-Morales
We introduce stochastic variants of the classical Bernstein polynomials associated with a continuous function f, built up from a general triangular array of random variables. We discuss the uniform convergence in probability of the approximation process that they represent, providing at the same time rates of convergence. In the particular case in which the triangular array of random variables con...... hiện toàn bộ
Reduced basis methods with adaptive snapshot computationsSpringer Science and Business Media LLC - Tập 43 - Trang 257-294 - 2016
Mazen Ali, Kristina Steih, Karsten Urban
We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB ‘truth space’, but allow for error estimation of the RB approximation with respect to the exact solution of the co...... hiện toàn bộ
Blossoms and Optimal BasesSpringer Science and Business Media LLC - - 2004
Marie-Laurence Mazure
It is now classical to define blossoms by means of intersections of osculating flats. We consider here the most general context of spline spaces with sections in arbitrary extended Chebyshev spaces and with connections defined by arbitrary lower triangular matrices with positive diagonal elements. We show how the existence of blossoms in such spaces automatically leads to optimal bases in the sens...... hiện toàn bộ
Classification of Bivariate Configurations with Simple Lagrange Interpolation FormulaeSpringer Science and Business Media LLC - Tập 20 - Trang 5-16 - 2004
J.M. Carnicer, M. Gasca
In 1977 Chung and Yao introduced a geometric characterization in multivariate interpolation in order to identify distributions of points such that the Lagrange functions are products of real polynomials of first degree. We discuss and describe completely all these configurations up to degree 4 in the bivariate case. The number of lines containing more nodes than the degree is used for classifying ...... hiện toàn bộ
Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equationsSpringer Science and Business Media LLC - Tập 28 - Trang 383-399 - 2007
Chengjian Zhang, Stefan Vandewalle
This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability criteria are constructed for...... hiện toàn bộ
An adaptive multiscale hybrid-mixed method for the Oseen equationsSpringer Science and Business Media LLC - Tập 47 - Trang 1-36 - 2021
Rodolfo Araya, Cristian Cárcamo, Abner H. Poza, Frédéric Valentin
A novel residual a posteriori error estimator for the Oseen equations achieves efficiency and reliability by including multilevel contributions in its construction. Originates from the Multiscale Hybrid Mixed (MHM) method, the estimator combines residuals from the skeleton of the first-level partition of the domain, along with the contributions from element-wise approximations. The second-level es...... hiện toàn bộ