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Interp: Cheby/error connection: showlater
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inducer committed Nov 19, 2024
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Expand Up @@ -5049,7 +5049,7 @@ and an auxiliary function:
*** Error Result: Connection to Chebyshev

What is the connection between the error result and Chebyshev interpolation?
#+LATEX: \begin{hidden}
#+LATEX: \begin{showlater}
- The error bound suggests choosing the interpolation nodes such that the product
\(\abs{\prod_{i=1}^n (x-x_i)}\) is as small as possible. The Chebyshev nodes achieve this.

Expand All @@ -5058,7 +5058,7 @@ What is the connection between the error result and Chebyshev interpolation?
- Confusing: /Chebyshev approximating polynomial/ (or "polynomial best-approximation").
*Not* the Chebyshev interpolant.
- Chebyshev nodes also do *not* minimize the Lebesgue constant.
#+LATEX: \end{hidden}
#+LATEX: \end{showlater}

\demolink{interpolation}{Chebyshev Interpolation} (Part V)

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