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arXiv · 2507.04747

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

Rashid A. Aliev·Vugar A. Guliyev·Amil F. Jabiyev
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Abstract

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

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Rashid A. Aliev, Vugar A. Guliyev, Amil F. Jabiyev. 2025-07-07. Best approximation of a three-variable function by sum of one-variable coordinate functions. https://arxiv.org/abs/2507.04747

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