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