approximation by polynomials

  • 1Approximation theory — In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on …

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  • 2Approximation theory/Proofs — Proof that an N th degree polynomial that gives rise to an error function that has N + 2 maxima, of alternating signs and equal magnitudes, is optimal in the sense of approximation theory. Such an optimal polynomial gives the minimum value, over… …

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  • 3Chebyshev polynomials — Not to be confused with discrete Chebyshev polynomials. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev,[1] are a sequence of orthogonal polynomials which are related to de Moivre s formula and which can be defined… …

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  • 4Hermite polynomials — In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical… …

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  • 5Discrete Chebyshev polynomials — Not to be confused with Chebyshev polynomials. In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by Pafnuty Chebyshev (1864) and… …

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  • 6Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… …

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  • 7Classical orthogonal polynomials — In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical… …

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  • 8Calculus with polynomials — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …

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  • 9List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …

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  • 10Mergelyan's theorem — is a famous result from complex analysis, a branch of mathematics, named after the Armenian mathematician Sergei Nikitovich Mergelyan (May 19, 1928 August 20, 2008) and was put forward by him in 1951. It states the following: Let K be a compact… …

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