Best approximation of a three-variable function by sum of one-variable coordinate functions

2025/07/07 by Aliev, Rashid A., Guliyev, Vugar A., Jabiyev, Amil F.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.04747

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,Ω)=inf||f(x,y,z)-ϕ(x)-ψ(y)-ω(z)||_∞=? 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.

Citations

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