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In 1952, Cornelius Lanczos showed that the Chebyshev polynomials are important in approximation theory for the solution of linear systems; [2] the roots of T n (x), which are also called Chebyshev nodes, are used as matching points for optimizing polynomial interpolation.
Chebyshev approximation is the basis for Clenshaw–Curtis quadrature, a numerical integration technique. ... "Chebyshev Polynomials in Numerical Analysis." Oxford ...
The Chebyshev nodes of the second kind, also called the Chebyshev extrema, are the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the second kind. Both of these sets of numbers are commonly referred to as Chebyshev nodes in literature. [1] Polynomial interpolants constructed from ...
A typical example of a Chebyshev space is the subspace of Chebyshev polynomials of order n in the space of real continuous functions on an interval, C[a, b]. The polynomial of best approximation within a given subspace is defined to be the one that minimizes the maximum absolute difference between the polynomial and the function.
In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by Pafnuty Chebyshev [1] and rediscovered by Gram. [2] They were later found to be applicable to various algebraic properties of spin angular momentum.
Chebyshev Polynomials: From Approximation Theory to Algebra and Number Theory. NY: Wiley. 1990; 249 pages, revised 2nd edition of The Chebyshev Polynomials ; addition of about 80 exercises, a chapter introducing some elementary algebraic and number theoretic properties of the Chebyshev polynomials, and additional coverage of the polynomials ...
Polynomial expansions such as the Taylor series expansion are often convenient for theoretical work but less useful for practical applications. Truncated Chebyshev series, however, closely approximate the minimax polynomial. One popular minimax approximation algorithm is the Remez algorithm.
In mathematics, approximation theory is concerned with how functions can be approximated with other, simpler, ... Chebyshev polynomials; Elliott Ward Cheney Jr.