Abstract

It is well known that the adaptive algorithm is simple and easy to program but the results are not fully competitive with other nonlinear methods such as free knot spline approximation. We modify the algorithm to take full advantages of nonlinear approximation. The new algorithms have the same approximation order as other nonlinear methods, which is proved by characterizing their approximation spaces. One of our algorithms is implemented on the computer, with numerical results illustrated by figures and tables.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1137/S0036142999353569

Rights Information

© Society for Industrial and Applied Mathematics

Keywords

Adaptive algorithms, Approximation spaces, Besov spaces, Data reduction, Degree of approximation, Modulus of smoothness, Nonlinear approximation, Piecewise polynomials, Splines

Publication Date

12-1-2001

Journal Title

SIAM Journal on Numerical Analysis

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