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除差表

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除差表

是否有一个包可以自动排版用于计算牛顿除差算法系数的三角表？

答案1

我在互联网上找到了一个对我有用的解决方案。如果你想看看我在哪里找到的，请使用关联，这是一篇关于有限差分的文本。

\[
\begin{array}{cccccc}
x_0 & y_0 \\
    &     & \Delta y_0 \\
x_1 & y_1 &             & \Delta^2 y_0\\
    &     & \Delta y_1  &              & \Delta^3 y_0\\
x_2 & y_2 &             & \Delta^2 y_1 &             & \Delta^4 y_0\\
    &     & \Delta y_2  &              & \Delta^3 y_1\\
x_3 & y_3 &             & \Delta^2 y_2\\
    &     & \Delta y_3 \\
x_4 & y_4
\end{array}
\]

答案2

我今天早上也遇到了同样的问题。我用一个不太优雅的安排解决了它

\documentclass[a4paper,11pt]{article}

\usepackage{array}
\newcolumntype{C}{>{$}c<{$}}

\begin{document}

\begin{table}[h]
    \centering
    \begin{tabular}{C}
        \begin{tabular}{C|C|C|C|C|C|C|C|C}
           x_1,x_2 & x_1,x_3 & x_1,x_4 & x_1, x_5 & x_1, x_6 & x_1, x_7 & x_1, x_8 & x_1, x_9 & x_1, x_{10} 
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C|C|C|C|C|C}
           x_2,x_3 & x_2,x_4 & x_2,x_5 & x_2,x_6 & x_2,x_7 & x_2,x_8 & x_2,x_9 & x_2,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C|C|C|C|C}
           x_3,x_4 & x_3,x_5 & x_3,x_6 & x_3,x_7 & x_3,x_8 & x_3,x_9 & x_3,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C|C|C|C}
           x_4,x_5 & x_4,x_6 & x_4,x_7 & x_4,x_8 & x_4,x_9 & x_4,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C|C|C}
           x_5,x_6 & x_5,x_7 & x_5,x_8 & x_5,x_9 & x_5,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C|C}
           x_6,x_7 & x_6,x_8 & x_6,x_9 & x_6,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C|C}
           x_7,x_8 & x_7,x_9 & x_7,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C|C}
           x_8,x_9 & x_8,x_{10}
        \end{tabular}
        \\ 
        \begin{tabular}{C}
           x_9,x_{10}
        \end{tabular}
    \end{tabular}
    \caption{Divided Differences}
    \label{table:divided_differences}
\end{table}
\end{document}

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