The convergence of the best discrete linear \(L_ p\) approximation as p\(\to 1\) (Q1061967)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The convergence of the best discrete linear \(L_ p\) approximation as p\(\to 1\) |
scientific article; zbMATH DE number 3910995
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The convergence of the best discrete linear \(L_ p\) approximation as p\(\to 1\) |
scientific article; zbMATH DE number 3910995 |
Statements
The convergence of the best discrete linear \(L_ p\) approximation as p\(\to 1\) (English)
0 references
1983
0 references
It is well known that the best discrete linear \(L_ p\) approximation converges to a special best Chebyshev approximation as \(p\to \infty\). In this paper it is shown that the corresponding result for the case \(p\to 1\) is also true. Furthermore, the special best \(L_ 1\) approximation obtained as the limit is characterized as the unique solution of a nonlinear programming problem on the set of all \(L_ 1\) solutions.
0 references
best Chebyshev approximation
0 references
nonlinear programming problem
0 references
