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  Encyclopedia of Keywords > Polynomial Interpolation > Chebyshev Nodes   Michael Charnine

Keywords and Sections
FORMULAS
ROOTS
EQUIDISTANT
OSCILLATION
NODES
POLYNOMIAL INTERPOLATION
CHEBYSHEV NODES
Review of Short Phrases and Links

    This Review contains major "Chebyshev Nodes"- related terms, short phrases and links grouped together in the form of Encyclopedia article.

Definitions

  1. The Chebyshev nodes are important in approximation theory because they form a particularly good set of nodes for polynomial interpolation.
  2. All Chebyshev nodes are contained in the interval [−1, 1]. To get nodes over an arbitrary interval [ a, b] a linear transformation can be used. (Web site)

Formulas

  1. The formulas of the Chebyshev nodes in the text do not seem to be correct, including the formula used in Computer Problem 10, Section 4.2, p.

Roots

  1. In numerical analysis, Chebyshev nodes are the roots of the Chebyshev polynomial of the first kind.

Equidistant

  1. O(N) algorithms for special cases (equidistant, Chebyshev nodes).

Oscillation

  1. This oscillation is lessened by choosing interpolation points at Chebyshev nodes.
  2. The oscillation can be minimized by using Chebyshev nodes instead of equidistant nodes.

Nodes

  1. All Chebyshev nodes are contained in the interval [−1, 1]. To get nodes over an arbitrary interval [ a, b] a linear transformation can be used. (Web site)

Polynomial Interpolation

  1. The Chebyshev nodes are important in approximation theory because they form a particularly good set of nodes for polynomial interpolation. (Web site)

Chebyshev Nodes

  1. For every absolutely continuous function on [−1, 1] the sequence of interpolating polynomials constructed on Chebyshev nodes converges to f(x) uniformly. (Web site)
  2. The roots are sometimes called Chebyshev nodes because they are used as nodes in polynomial interpolation.
  3. We conclude again that Chebyshev nodes are a very good choice for polynomial interpolation, as the growth in n is exponential for equidistant nodes. (Web site)

Categories

  1. Polynomial Interpolation
  2. Nodes
  3. Continuous Function
  4. Uniformly
  5. Oscillation
  6. Books about "Chebyshev Nodes" in Amazon.com

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  Short phrases about "Chebyshev Nodes"
  Originally created: March 20, 2008.
  Links checked: February 13, 2013.
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