Vabishchevich P. N.

This work addresses the problem of single-variable function approximation within the class of nonlinear approximations with two sets of parameters. The approximating function is linear with respect to the first parameter (which is constrained to be positive), while each term of the approximating function represents a given function with nonlinear dependence on the second parameter. The computational algorithm is based on residual minimization in Hilbert space. The first key aspect of the developed approach involves effectively reducing the problem to a standard linear best approximation problem by discretizing the second parameter over an extended set of points within the admissible segment. The second key feature lies in determining the set of linear approximation parameters at each iteration of the classical non-negative least squares (NNLS) method. Numerical results are presented to demonstrate the capabilities of this computational algorithm for nonlinear function approximation.