7 citations · 10 across the 13 of their papers we have counts for
13 papers
Non-linear WENO B-spline based approximation method
Sergio Amat, David Levin, Juan Ruiz-Álvarez +1
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline fun…
Numerical integration rules with improved accuracy close to singularities
Sergio Amat, Zhilin Li, Juan Ruiz-Alvarez +2
Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincid…
Geometric representation of the weighted harmonic mean of positive values and potential uses
S. Amat, P. Ortiz, J. Ruiz +2
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of positive real numbers. Together with th…
A nonlinear PPH-type reconstruction based on equilateral triangles
S. Amat, P. Ortiz, J. Ruiz +2
In this paper we introduce a new nonlinear reconstruction operator over two dimensional triangularized domains with equilateral triangles. We focus on the local definition of the o…
Global and explicit approximation of piecewise smooth 2D functions from cell-average data
Sergio Amat, David Levin, Juan Ruiz-Alvarez +1
Given cell-average data values of a piecewise smooth bivariate function within a domain , we look for a piecewise adaptive approximation to . We are interested in an expl…
Explicit multivariate approximations from cell-average data
Sergio Amat, David Levin, Juan Ruiz-Alvarez +1
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. On…
Corrected approximation strategy for piecewise smooth bivariate functions
Sergio Amat, David Levin, Juan Ruiz-Álvarez
Given values of a piecewise smooth function on a square grid within a domain , we look for a piecewise adaptive approximation to . Standard approximation techniques achie…
On a regularization-correction approach for the approximation of piecewise smooth functions
Sergio Amat, David Levin, Juan Ruiz-Álvarez
Linear approximation approaches suffer from Gibbs oscillations when approximating functions with singularities. ENO-SR resolution is a local approach avoiding oscillations and with…
Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing
Sergio Amat, Juan Ruiz, Chi-Wang Shu +1
In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Yáñez, A new WENO-2r algorit…
A new WENO-2r algorithm with progressive order of accuracy close to discontinuities
Sergio Amat, Juan Ruiz, Chi-Wang Shu +1
In this article we present a modification of the algorithm for data discretized in the point values introduced in [S. Amat, J. Ruiz, C.-W. Shu, On a new WENO algorithm of order 2r…
On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods
Miquel Grau-Sánchez, Miquel Noguera, Sergio Amat
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostr…
On a C2-nonlinear subdivision scheme avoiding Gibbs oscillations
Sergio Amat, Karine Dadourian, Jacques Liandrat
This paper is devoted to the presentation and the analysis of a new nonlinear subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stabi…
Analysis of a class of non linear subdivision schemes and associated multi-resolution transforms
S. Amat, K. Dadourian, J. Liandrat
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as…