Commit d5160090 authored by Conor McCoid's avatar Conor McCoid
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Extrap: minor fixes to notes.tex

parent 40598751
......@@ -390,7 +390,7 @@ s_{n,k} - s_{n,k} = & \sum_{j=0}^m \gamma_j \left ( x_{n+j+i+1} - x_{n+j+i} \rig
for the same set of $i$.
This gives the following linear equation:
\begin{equation*}
\begin{bmatrix} 1 & \dots & 1 \\ r_n & \dots & r_{n+m} \\ \vdots & & \vdots \\ r_{n+2k-m-1} & \dots & r_{n+2k} \end{bmatrix} \begin{bmatrix} \gamma_0 \\ \vdots \\ \gamma_m \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ \vdots \\ 0 \end{bmatrix}.
\begin{bmatrix} 1 & \dots & 1 \\ r_n & \dots & r_{n+m} \\ \vdots & & \vdots \\ r_{n+2k-m-1} & \dots & r_{n+2k-1} \end{bmatrix} \begin{bmatrix} \gamma_0 \\ \vdots \\ \gamma_m \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ \vdots \\ 0 \end{bmatrix}.
\end{equation*}
For this equation to be solvable one requires that $2k-m = m$, or $m=k$.
The solution is then
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