In numerical analysis, **Chebyshev nodes** are the roots of the Chebyshev polynomial of the first kind. They are often used as nodes in polynomial interpolation because the resulting interpolation polynomial minimizes the Runge's phenomenon.

Read more about Chebyshev Nodes: Definition, Approximation Using Chebyshev Nodes

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Approximation Using

... The

**Chebyshev Nodes**... The

**Chebyshev nodes**are important in approximation theory because they form a particularly good set of**nodes**for polynomial interpolation ... This bound is attained by the scaled**Chebyshev**polynomials 21−n Tn, which are also monic ... When interpolation**nodes**xi are the roots of the Tn, the interpolation error satisfies therefore ...Lebesgue Constant (interpolation) - Minimal Lebesgue Constants

... In the case of equidistant

... In the case of equidistant

**nodes**, the Lebesgue constant grows exponentially ... other hand, the Lebesgue constant grows only logarithmically if**Chebyshev nodes**are used, since we have where a = 0.9625… ... We conclude again that**Chebyshev nodes**are a very good choice for polynomial interpolation ...### Famous quotes containing the word nodes:

“There are characters which are continually creating collisions and *nodes* for themselves in dramas which nobody is prepared to act with them. Their susceptibilities will clash against objects that remain innocently quiet.”

—George Eliot [Mary Ann (or Marian)

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