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In computational practice, most attention is paid to rational approximationsof functions and approximations by the sum of exponents. We consider a wideenough class of nonlinear approximations characterized by a set of two requiredparameters. The approximating function is linear in the first parameter; theseparameters are assumed to be positive. The individual terms of theapproximating function represent a fixed function that depends nonlinearly onthe second parameter. A numerical approximation minimizes the residualfunctional by approximating function values at individual points. The secondparameter's value is set on a more extensive set of points of the interval ofpermissible values. The proposed approach's key feature consists in determiningthe first parameter on each separate iteration of the classical non-negativeleast squares method. The computational algorithm is used to rationalapproximate the function $x^{-\alpha}, \ 0 < \alpha < 1, \ x \geq 1$. Thesecond example concerns the approximation of the stretching exponentialfunction $\exp(- x^{\alpha} ), \ \ \quad 0 < \alpha < 1$ at $ x \geq 0$ by thesum of exponents.

Nonlinear approximation of functions based on non-negative least squares solver