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Stochastic Bernstein polynomials: uniform convergence in probability with rates
Springer Science and Business Media LLC - Tập 46 - Trang 1-10 - 2020
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...
An approximation of Daubechies wavelet matrices by perfect reconstruction filter banks with rational coefficients
Springer Science and Business Media LLC - Tập 38 - Trang 147-158 - 2011
It is described how the coefficients of Daubechies wavelet matrices can be
approximated by rational numbers in such a way that the perfect reconstruction
property of the filter bank be preserved exactly.
Reduced basis methods with adaptive snapshot computations
Springer Science and Business Media LLC - Tập 43 - Trang 257-294 - 2016
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...
Blossoms and Optimal Bases
Springer Science and Business Media LLC - - 2004
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...
Classification of Bivariate Configurations with Simple Lagrange Interpolation Formulae
Springer Science and Business Media LLC - Tập 20 - Trang 5-16 - 2004
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 ...
The regularizing properties of the composite trapezoidal method for weakly singular Volterra integral equations of the first kind
Springer Science and Business Media LLC - Tập 36 - Trang 331-351 - 2011
In the present paper we investigate the regularizing properties of the product
trapezoidal method for solving weakly singular first kind Volterra integral
equations with perturbed right-hand sides. Some numerical results are also
presented.
Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations
Springer Science and Business Media LLC - Tập 28 - Trang 383-399 - 2007
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...
An adaptive multiscale hybrid-mixed method for the Oseen equations
Springer Science and Business Media LLC - Tập 47 - Trang 1-36 - 2021
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...
Adaptive energy preserving methods for partial differential equations
Springer Science and Business Media LLC - - 2018
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