Approximations and expansions Approximation by linear operators Concept
Lebesgue constant
Summary
The Lebesgue constant of a set of interpolation nodes measures how much polynomial interpolation at these nodes can amplify errors. It is the operator norm of the interpolation map on continuous functions with the uniform norm. It compares the interpolation error with the error of best approximation, and it measures the sensitivity of interpolation to errors in the data. For equally spaced nodes it grows exponentially with the degree, while for Chebyshev nodes it grows only like a logarithm.
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| Tag | 7V7KWNK9HN |
|---|---|
| URI | m2://7V7KWNK9HN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 41A05, 65D05, 41A10 |
| Same as |
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