| 1. | However, polynomial interpolation also has some disadvantages.
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| 2. | We conclude again that Chebyshev nodes are a very good choice for polynomial interpolation.
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| 3. | So, we see that polynomial interpolation overcomes most of the problems of linear interpolation.
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| 4. | It is a special case of polynomial interpolation with " n " = 1.
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| 5. | This consisted of algebra with numerical methods, polynomial interpolation and its applications, and indeterminate integer equations.
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| 6. | Additionally, the interpolating polynomial is unique, as shown by the unisolvence theorem at the polynomial interpolation article.
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| 7. | Polynomial interpolation can estimate local maxima and minima that are outside the range of the samples, unlike linear interpolation.
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| 8. | The Chebyshev nodes are important in approximation theory because they form a particularly good set of nodes for polynomial interpolation.
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| 9. | Furthermore, polynomial interpolation may exhibit oscillatory artifacts, especially at the end points ( see Runge's phenomenon ).
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| 10. | This can be seen as a form of polynomial interpolation with harmonic base functions, see trigonometric interpolation and trigonometric polynomial.
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