Computing Best lp Approximations by Functions Nonlinear in One Parameter

Abstract

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 + a 2 ef :x , a\ + a 2 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.