Adaptive approximation

Adaptive Approximation

Adaptive Approximation of Curves

We propose adaptive multiscale refinement algorithms for approximating and encoding curves by polygonal curves. We establish rates of approximation of these algorithms in the Hausdorff metric. For example, we show that under the mere assumption that the original curve has finite length then the first of these algorithms gives a rate of convergence O(1/n) where n is the number of vertices of the...

Degree of Adaptive Approximation

We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.

Adaptive Weak Approximation

adaptive mesh generation for approximation of traffic flow equations

this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...