Chebyshev Nodes

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 NodesDefinition, Approximation Using Chebyshev Nodes

Other articles related to "chebyshev nodes, nodes, chebyshev":

Approximation Using 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 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 ...

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