Exercise 4.3.10

Answers

[\begin{matrix} 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \end{matrix}] [\begin{matrix} C \\ D \\ E \\ F \end{matrix}] = [\begin{matrix} 0 \\ 8 \\ 8 \\ 20 \end{matrix}] .

Then

[\begin{matrix} C \\ D \\ E \\ F \end{matrix}] = \frac{1}{3} [\begin{matrix} 0 \\ 47 \\ - 28 \\ 5 \end{matrix}]

Exact cubic so $p = b, e = 0 .$ This Vandermonde matrix gives exact interpolation by a cubic at $0, 1, 3, 4$ .

mathchakra

2023-09-14 08:10