Nonlinear Chebyshev fitting from the solution of ordinary differential equations (Q1315211)

The nonlinear Chebyshev approximation of real-valued data is considered where the approximating functions are generated from the solution of parameter dependent initial value problems \(dy/dx = f(x,y,p)\), \(x\in [a,b]\), \(y(a) = p_ 1\) and \(p = (p_ 1,p_ 2,\dots,p_ n)\in P\subset \mathbb{R}^ n\). The authors also give a much simplified proof of the local Haar condition. Some algorithm details are described along with five numerical examples of best approximations computed by the exchange algorithm and a Gauss-Newton type method. In case good starting approximations are available, the exchange algorithm performs well, requiring only a few iterations.