Best approximation of a three-variable function by sum of one-variable coordinate functions
Abstract
Consider the following approximation problem of a continuous function of three variables by the sum of three continuous functions of one variable: \[ E(f,)=∈f||f(x,y,z)-φ(x)-(y)-ω(z)||∞=? \] where f(x,y,z) is a given continuous function defined on =[0,1]3 and the infimum runs over all triplets of continuous functions φ(x),(y),ω(z) defined on the unit interval [0,1]. In this paper, we will prove a formula to calculate the error E(f,) under certain conditions.
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