Computing Best l_p Approximations by Functions Nonlinear in one Parameter

This paper describes an algorithm for computing best l\, k and /(D approximations to discrete data, by functions of several parameters which depend nonlinearly on just one of these parameters. Such functions (e.g. «i + a2ef , a\ + a2 sin ex, (ai + a2x)l(l + ex)) often occur in practice, and a numerical study confirms that it is feasible to compute best approximations in any of the above norms when using these functions. Some remarks on the theory of best h approximations by these functions are included.