Computational Algorithm for Nonlinear Approximation of Functions

We consider the problem of approximating functions of one variable within the class of nonlinear approximations with a set of two required parameters. The approximating function is linear in the first parameter; these parameters are assumed to be positive. The individual terms of the approximating function represent a given function that depends nonlinearly on the second parameter. The computational algorithm is based on residual minimization in a Hilbert space. The first key point of the developed approach is related to the actual transition to a standard linear problem of best approximation of functions when the second parameter is given on an extended set of points within the interval of permissible values. The second key point consists in determining the set of linear approximation parameters at each separate iteration of the classical nonnegative least squares (NNLS) method. Numerical results are presented that illustrate the capabilities of this computational algorithm for nonlinear approximation of functions.