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Newton Raphson Method LaTeX

如何在LaTeX中实现Newton Raphson方法？

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\\documentclass{article}
\\usepackage[ngerman]{babel}
\\usepackage{xfp}
\\usepackage{tikz}

\
ewcount\\MaxIter
\
ewcount\\Counter
% the function
\
ewcommand{\\f}[1]{%
#1%
}
% first derivation of the function
\
ewcommand{\\df}[1]{%
1%
}
% the command
% 1. variable: max iterations
% 2. variable: start value x_0
\
ewcommand{\
ewtonRaphson}[2][5]{
\\Counter=0%
\\MaxIter=#1%
\\pgfmathsetmacro{\\x}{#2}%
\\Loop%
}
% the loop
\
ewcommand{\\Loop}{%
\\let\
ext= \\Loop%
\\pgfmathsetmacro{\\tempf}{\\fpeval{\\f{\\x}}}%
\\pgfmathsetmacro{\\tempdf}{\\fpeval{\\df{\\x}}}%
\\pgfmathsetmacro{\\x}{\\fpeval{\\x-\\tempf/\\tempdf}}%
\\ifnum\\Counter<\\MaxIter \\advance\\Counter by 1 \\else \\let\
ext=\
elax \\fi%
\
ext%
}

\\begin{document}
% set function
\
enewcommand{\\f}[1]{%
#1^2-2%
}
% set first derivation
\
enewcommand{\\df}[1]{%
2*#1%
}
% calculate
\
ewtonRaphson[10]{0.5}
% print
\\pgfmathprintnumber[precision=10]{\\x}
\\end{document}