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Next: $B$3$NJ8=q$K$D$$$F(B... (PDF ե: system1.pdf)

$BJ?@.(B 13 $BG/(B 7 $B7n(B 18 $BF|(B
$B2a>j$JO"N)0l.<+>h2r(B
$B?73c9)2JBg3X(B $B>pJsEE;R9)3X2J(B $BC]LnLP<#(B

$B2a>j$JO"N)0l

\begin{displaymath}
\begin{array}{ll}
A \mbox{\boldmath$x$} = \mbox{\boldmath$b...
...
\mbox{\boldmath$b$} = {}^T\!(b_1,b_2,\ldots,b_m)
\end{array}\end{displaymath}

($m>n$) $B$O!"0lHL$K$O2r$r;}$D$H$O8B$i$J$$!#$3$l$N:G>.<+>h2r!"$9$J$o$A(B $B<+>h8m:9(B

\begin{displaymath}
Err = \sum_{k=1}^{m}(\mbox{\boldmath$\alpha$}_k \mbox{\boldm...
...( \mbox{\boldmath$\alpha$}_k = (a_{k1},a_{k2},\ldots ,a_{kn}))
\end{displaymath}

$B$r:G>.$K$9$k(B $\mbox{\boldmath$x$}$ $B$r5a$a$k$3$H$r9M$($k!#(B


$BL?Bj(B 1

$B$=$N$h$&$J(B $\mbox{\boldmath$x$}$ $B$,$?$@0l$D$K7h$^$k$N$O!"(B$A$ $B$NNs%Y%/%H%k(B

\begin{displaymath}
\mbox{\boldmath$\beta$}_1,\mbox{\boldmath$\beta$}_2,\ldots,...
...mbox{\boldmath$\beta$}_k={}^T\!(a_{1k},a_{2k},\ldots,a_{mk}))
\end{displaymath}

$B$,0ll9g!"$=$N$h$&$J(B $\mbox{\boldmath$x$}$ $B$OO"N)J}Dx<0(B

\begin{displaymath}
{}^T\!A A\mbox{\boldmath$x$} = {}^T\!A\mbox{\boldmath$b$}
\end{displaymath}

$B$GM?$($i$l$k!#(B


$B>ZL@(B

$B0lHL$N>l9g$bF1MM$J$N$G!"(B$n=2$, $m=3$ $B$G9T$&!#J}Dx<0$r(B

\begin{displaymath}
\left\{
\begin{array}{lll}
ax+by & = & p\\
cx+dy & = & q\\
ex+fy & = & r
\end{array} \right.
\end{displaymath}

$B$H$7$F9M$($k!#$D$^$j$3$N>l9g(B

\begin{displaymath}
A = \left[\begin{array}{ll}a & b\\ c & d \\ e & f\end{array...
...ath$x$}={}^T\!(x,y),
\ \ \ \mbox{\boldmath$b$}={}^T\!(p,q,r)
\end{displaymath}

$B$G$"$k!#<+>h8m:9$O(B

\begin{displaymath}
Err=(ax+by-p)^2+(cx+dy-q)^2+(ex+fy-r)^2
\end{displaymath}

$B$G$"$k!#(B2 $BJQ?t4X?t$N6KBg6K>.$NM}O@$K$h$j!"$=$N:G>.CM$rM?$($kDdN1E@$O(B

\begin{displaymath}
\frac{\partial Err}{\partial x}=
\frac{\partial Err}{\partial y}=0
\end{displaymath}

$B$H$J$kE@(B $(x,y)$ $B$G$"$j!"(B

\begin{eqnarray*}\frac{\partial Err}{\partial x}
& = & 2a(ax+by-p) + 2c(cx+dy-...
...rr}{\partial y}
& = & 2b(ax+by-p) + 2d(cx+dy-q) + 2f(ex+fy-r)
\end{eqnarray*}



$B$J$N$G!"$h$C$F!"(B

\begin{eqnarray*}&&
\left[\begin{array}{l}
a(ax+by-p) + c(cx+dy-q) + e(ex+fy-r...
...ath$b$}\\
& = & \left[\begin{array}{l}0\\ 0\end{array}\right]
\end{eqnarray*}



$B$rK~$?$9$b$N$,$=$NDdN1E@$H$J$k!#(B

\begin{eqnarray*}\det({}^T\!A A)
& = & \left\vert
\left[\begin{array}{lll}a &...
...2+d^2+f^2)-(ab+cd+ef)^2\\
& = & (ad-cb)^2+(af-eb)^2+(cf-ed)^2
\end{eqnarray*}



$B$J$N$G!"$3$l$,(B 0 $B$K$J$k$N$O(B $ad=cb$, $af=eb$, $cf=ed$, $B$9$J$o$A(B $a:c:e=b:d:f$ $B$H$J$k$H$-!"$D$^$j(B $A$ $B$NNs%Y%/%H%k(B ${}^T\!(a,c,e)$ $B$H(B ${}^T\!(b,d,f)$ $B$,J?9T$G$"$k$H$-!"$H$J$k!#(B

$B$=$l0J30$N>l9g$K$OJ}Dx<0(B ${}^T\!A A\mbox{\boldmath$x$}-{}^T\!A\mbox{\boldmath$b$}=0$ $B$K$h$C$F0l0U$KDdN1E@$,5a$^$k!#(B





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Next: $B$3$NJ8=q$K$D$$$F(B...
Shigeharu TAKENO
2001$BG/(B 8$B7n(B 17$BF|(B