Chebyshev alternation theorem
GPTKB entity
Statements (12)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
continuous functions on closed intervals
|
| gptkbp:concerns |
polynomial approximation
best uniform approximation |
| gptkbp:field |
approximation theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev alternation theorem
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:state |
A polynomial of degree n is the best uniform approximation to a continuous function on a closed interval if and only if the error function attains its maximum absolute value at least n+2 times with alternating signs.
|
| gptkbp:usedIn |
numerical analysis
minimax approximation |
| gptkbp:bfsParent |
gptkb:Remez_exchange_algorithm
|
| gptkbp:bfsLayer |
7
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