On a conjecture for weighted interpolation using Chebyshev polynomials of the third and fourth kinds


Simon J. Smith


Abstract

carpathian_2006_22_147_151_abstract

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carpathian_2006_22_147_151

A conjecture for the projection norm (or Lebesgue constant) of a weighted interpolation method based on the zeros of Chebyshev polynomials of the third and fourth kinds is resolved. This conjecture was made in a paper by J. C. Mason and G. H. Elliott in 1995. The proof of the conjecture is achieved by relating the projection norm to that of a weighted interpolation method based on zeros of Chebyshev polynomials of the second kind.

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Author(s)

J. Smith, Simon