% $BI=Bj(B: $B<}B+>r7o(B
%
% $BMzNr(B: 2004-07-13 $B?y;39L0lO/(B



\section{$B?tCM7W;;$K$*$1$k8m:9(B}

$B?tCM8m:9$r@8$8$k$3$H$N$J$$7W;;$r(B{\bf $BM}O@7W;;(B}$B$H8F$V$3$H$K$7$h$&(B. 
$BM}O@7W;;$H$O(B, $B$$$o$PL58B7e7W;;$G$"$k(B. $B?tCM7W;;$K$*$$$F$OIbF0>.?tE@(B 10 $B?J(B
6 $B7e(B($BC1@:EY(B), $B$b$7$/$O(B 10 $B?J(B 15 $B7e(B($BG\@:EY(B)$BDxEY$NM-8z7e?tCM$rMQ$$$F7W;;$9(B
$B$k$N$G(B, $B8m:9$OHr$1$,$?$$(B. $B8m:9$,>.$5$$$&$A$O<BMQ>e:$Fq$,@8$8$k$3$H$OL5$$(B
$B$,(B, $BBg$-$/$J$k$H?tCM7W;;$N7k2L$,?.Mj$G$-$J$$$b$N$H$J$k(B. 

$B$"$k?t$N??CM$r(B $a$, $B6a;w2r$r(B $x$ $B$H$9$k$H$-(B, 
%
\begin{eqnarray}
 e = x - a
\end{eqnarray}
%
$B$r(B{\bf $B8m:9(B}(error)$B$H$$$&(B. $B8m:9$N@dBPCM(B
%
\begin{eqnarray}
 |e| = |x - a|
\end{eqnarray}
%
$B$r(B{\bf $B@dBP8m:9(B}(absolute error)$B$H$$$&(B. 

$B8m:9(B $e$ $B$,??$NCM(B $a$ $B$H2?7e$^$G$"$C$F$$$k$+$r<($9$?$a$K(B, 
$B8m:9$H??$NCM$H$NHf(B
%
\begin{eqnarray}
 e_{R} = \frac{e}{a} = \frac{x - a}{a}
\end{eqnarray}
%
$B$r(B{\bf $BAjBP8m:9(B}(relative error)$B$H$$$&(B. $e_{R}$ $B$,(B $10^{-5}$ $B$G$"$k$J$i$P(B,
$x$ $B$O(B 10 $B?J(B 5 $B7e$N@:EY$r;}$D$3$H$r0UL#$9$k(B. $B$?$@$7(B, $B??$NCM$,(B 0 $B$"$k$$$O(B
0 $B$K6a$$;~$K$O8m:9$NDxEY$rAjBP8m:9$G8@$$I=$9$3$H$,$G$-$:(B, $B@dBP8m:9$G8@$$(B
$BI=$5$M$P$J$i$J$$(B. 


\subsection{$B5vMF8m:9(B}

$B@dBP8m:9$,$"$k>.$5$JCM(B $\varepsilon_{A}$ $B$h$j$b>.$5$$$H$-(B, $B6a;wCM(B $x$ $B$r(B
$B??$NCM(B $a$ $B$NBe$o$j$KMQ$$$F$b$h$$$HH=CG$G$-$k(B. $B$3$N(B $\varepsilon_{A}$ $B$r(B
{\bf $B5vMF@dBP8m:9(B}(tollerable absolute error)$B$H8@$&(B.  $B$^$?AjBP8m:9$N@dBP(B
$BCM$,$"$k>.$5$JCM(B $\varepsilon_{R}$ $B$h$j$b>.$5$$$H$-(B, $B6a;wCM(B $x$ $B$r??$NCM(B 
$a$ $B$NBe$o$j$KMQ$$$F$b$h$$$HH=CG$G$-$k(B. $B$3$N(B $\varepsilon_{R}$ $B$r(B{\bf $B5v(B
$BMFAjBP8m:9(B}(tollerable relative error)$B$H8@$&(B. $B$3$l$i$N5vMF8m:9$ODL>o$O$8(B
$B$a$+$i$o$+$C$F$$$kCM$G$"$k(B. $B0J>e$r$^$H$a$k$H0J2<$N$h$&$K$J$k(B. 
%
\begin{eqnarray}
|x - a| < \varepsilon_{A},      && $B5vMF@dBP8m:9(B \\
|x - a| < \varepsilon_{R} |a|.  && $B5vMFAjBP8m:9(B 
\end{eqnarray}
%
$B$7$+$7(B, $|a|$ $B$,(B 0 $B$b$7$/$O(B 0 $B$K6a$$;~$K1s$$$H$-$K$bMxMQ$G$-$k8m:9$N4p=`(B
$B$H$7$F$O(B, 
%
\begin{eqnarray}
|x - a| < \varepsilon_{A} + \varepsilon_{R} |a|
\end{eqnarray}
%
$B$,<BMQE*$G$"$k(B. $B0lHL$K(B $a$ $B$O$o$+$C$F$$$J$$$+$i(B, $|a|$ $B$NBe$o$j$K(B $|x|$
$B$r;H$($P(B, 
%
\begin{eqnarray}
|x - a| < \varepsilon_{A} + \varepsilon_{R} |x|
\end{eqnarray}
%
$B$H$J$j(B, $B1&JU$,7W;;$G$-$k(B. 


$B5vMF8m:9$O(B, $B>.$5$1$l$P>.$5$$$[$I9b$$@:EY$rMW5a$9$k>r7o$K$J$C$F$$$k(B. $B:G$b(B
$B9b$$@:EY$G7W;;$9$k>l9g(B, 
%
\begin{description}
 \item[$B5vMF@dBP8m:9(B]~\\
	    $B7W;;5!$,5-21$G$-$k:G>.$N@dBPCM(B. 
	    7 $B%S%C%H;X?tIt$N7W;;5!$G$O(B $10^{-65} = 5.31890^{-79}$ $BDxEY$G(B
	    $B$"$k(B. 
%
 \item[$B5vMFAjBP8m:9(B]
	    $B7W;;5!$N(B 16 $B?J7e?t$N5U?t(B({\bf $B%^%7%s!&%$%W%7%m%s(B})$B$G(B, 
	    $B2>?tIt$,(B 16 $B?J(B 6 $B7e(B($BC1@:EY(B)$B$J$i$P(B, 
	    $16^{-(6-1)} = 9.537 \times 10^{-7}$, 
	    $B2>?tIt$,(B 16 $B?J(B 14 $B7e(B($BG\@:EY(B)$B$J$i$P(B, 
	    $16^{-(14-1)} = 2.220 \times 10^{-16}$ $B$G$"$k(B.  
\end{description}
%
$B$G$"$k(B. $B$3$l$i$N5vMF8m:9$h$j$b>.$5$J5vMF8m:9$rA*$V$3$H$K$O0UL#$,$J$$(B. 


\subsection{$B%K%e!<%H%sK!$N<}B+H=Dj(B}

$B%K%e!<%H%sK!$OE,Ev$J=i4|CM(B $x^{0}$ $B$+$i=PH/$7(B, $BH?I|E*$K6a;w2r(B $x^{k}$ $B$r(B
$B5a$a$k$b$N$G$"$k(B. $B%K%e!<%H%sK!$rMxMQ$9$k:]$K$O(B, $BE,Ev$J<}B+>r7o$r@_CV$7(B, 
$B6a;w2r$,??$NCM$K6a$/$J$C$?>l9g$K$OH?I|7W;;$r;_$a$k$H$$$&A`:n$,I,MW$H$J$k(B. 

$B??$NCM$,(B 0 $B$K6a$/$F$b1s$/$F$bMxMQ$G$-$k:G$bHFMQE*$O<}B+H=Dj>r7o$O(B, 
%
\begin{eqnarray}
 |x^{k+1} - x^{k}| < \varepsilon_{A} + \varepsilon_{R} (|x^{k}| + |x^{k+1}|)
\end{eqnarray}
%
$B$G$"$k(B. 