arXiv subjects

S. Amat

Publications and source records attributed to S. Amat.

4 recordsLinked to original sources

arXiv2022

A nonlinear PPH-type reconstruction based on equilateral triangles

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 operator. The ideas behind this definition come from some basic properties of the Harmonic mean of three positive values. We prove some results regarding the approximation properties of the operator and we carry out some numerical tests giving evidence of the avoidance of any Gibbs effects.

math.NA↗

arXiv2022

Geometric representation of the weighted harmonic mean of $n$ positive values and potential uses

This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that will allow us to define numerical approximation methods in several dimensions adapted to discontinuities.

math.NA↗

arXiv2015

On a Moser-Steffensen type method for nonlinear systems of equations

This paper is devoted to the construction and analysis of a Moser-Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence and finally we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.

math.NA↗

arXiv2008

Analysis of a class of non linear subdivision schemes and associated multi-resolution transforms

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 a perturbation of a linear subdivision scheme. Assuming a contractivity property, stability and convergence are derived. These results are then applied to various schemes such as uncentered interpolatory linear scheme, WENO scheme [13], Power-P scheme [16] and a non linear scheme using local spherical coordinates [18].

math.NA↗