Adaptive multiresolution analysis based on anisotropic triangulations

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm o...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of computation 2012-04, Vol.81 (278), p.789-810
Main Authors: COHEN, ALBERT, DYN, NIRA, HECHT, FRÉDÉRIC, MIREBEAU, JEAN-MARIE
Format: Article
Language:English
Subjects:
Approximation
Aspect ratio
Computer Science
Degrees of polynomials
Image compression
Mathematical functions
Mathematics
Numerical Analysis
Polynomials
Triangles
Triangulation
Vertices
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of f functions).
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2011-02495-6