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Consider the function $f(x)=|x|$ on $[-1,1]$. Given $n\neq0$, define $x_n^k=-1+\frac{2k}{n}$ for $0\leq k \leq n$. Let $g_n(x)$ be the unique polynomial of degree n which results by interpolating the data with $g_n(x_n^k)=f(x_n^k)$ for all $0\leq k \leq n$. Plot the sequence ${g_n(0.3)_{1\leq n \leq 20}}$

I understand how to find each $g_n$ separately by using the formula, but I'm not sure how to write code for this.

rrz.math
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1 Answers1

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I don't have access to matlab right now (and so I cannot test the code), but here goes the corresponding Wolfram Mathematica code:

g[x_, n_] := InterpolatingPolynomial[ Table[{-1 + 2*k/n, Abs[-1 + 2*k/n]}, {k, 0, n}], x];

ListPlot[Table[g[0.3, n], {n, 1, 20}], PlotRange -> Full]

enter image description here

PierreCarre
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