On the point for which the sum of the distances to \(n\) given points is minimum (Q1026585)
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scientific article; zbMATH DE number 5570714
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the point for which the sum of the distances to \(n\) given points is minimum |
scientific article; zbMATH DE number 5570714 |
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On the point for which the sum of the distances to \(n\) given points is minimum (English)
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25 June 2009
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This article presents a translation in English of a 1937 French article by \textit{E. Weiszfeld} (also known as Endre Vazsonyi, later on Andrew Vazsonyi) [Tohoku Math. J. 43, 355--386 (1937; JFM 63.0583.01; Zbl 0017.18007)]. The article begins with the statement of the theorem that is to be proven, which determines the properties of the point for which the sum of the distances to \(n\) given points is a minimum. After the statement of the theorem, the article presents three different proofs. The original terminology is used throughout this translation. The article concludes with an annex containing notes and comments by the translator.
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location problem
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Weber problem
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Euclidean distance
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Weiszfeld algorithm
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