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.
© Society for Industrial and Applied Mathematics
Adaptive algorithms, Approximation spaces, Besov spaces, Data reduction, Degree of approximation, Modulus of smoothness, Nonlinear approximation, Piecewise polynomials, Splines
Hu, Yingkang, Kirill A. Kopotun, and Xiang Ming Yu. "Modified adaptive algorithms." SIAM journal on numerical analysis 38, no. 3 (2000): 1013-1033.
SIAM Journal on Numerical Analysis