Discrete Nonlinear Mean Approximation

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Abstract Best approximation on a finite set by a non‐linear family of functions with respect to a general sum “norm”, which includes as a special case the Lp norms (1 < p < ∞), is considered. Properties of best approximations are given. It is shown that a local minimum of the error may not be a global minimum. Computation of best approximations is studied. Computational experience with approximation by a first degree polynomial plus an exponential with respect to the 3/2 power norm is discussed.