Best approximation of a three-variable function by sum of one-variable coordinate functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918259971850240 |
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| author | Aliev, Rashid A. Guliyev, Vugar A. Jabiyev, Amil F. |
| author_facet | Aliev, Rashid A. Guliyev, Vugar A. Jabiyev, Amil F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Best approximation of a three-variable function by sum of one-variable coordinate functions Aliev, Rashid A. Guliyev, Vugar A. Jabiyev, Amil F. Functional Analysis 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. |
| title | Best approximation of a three-variable function by sum of one-variable coordinate functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.04747 |