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Article #13550

Re: How to solve the LMI of symmetric matrix's semidefinite condition?

#13550
From: Hong Zhang
Date: Sat, 07 Sep 1996 00:00
52 lines
3257 bytes
from article <50q4v6$5vg@sakura.kudpc.kyoto-u.ac.jp>,
	by g52997@sakura.kudpc.kyoto-u.ac.jp (Tsukamoto, Chiaki):
|> $B9)A!Bg$NDMK\$G$9(B.

  $B>\:Y$J$42sEzM-Fq$&8f:B$$$^$7$?!#(B

|> In article <50op6f$j53@ces.ces.kyutech.ac.jp>
|> zhang@ces.ces.kyutech.ac.jp (Hong Zhang) writes:
|> >   $B$A$g$C$H$o$+$i$J$$$G$9$,!">e5-$NJ}K!$G$9$H!"(Bn(n+1)/2$B$NJQ(B
|> > $B?t$r5a$a$k$3$H$G$O$J$$$N$O!"0lHL@-$r<:$&62$l$,$"$k$G$O$J$$(B
|> > $B$+$H9M$($i$l$^$9!#$3$NE@$K$F!"$465<x$/$@$5$$!#(B
|> 
|> $BJ}Dx<0(B A X = \rho B $B$rK~$?$9$Y$7$H$$$&>r7o$+$i(B
|> A $B$N<+M3EY$O(B n(n-1)/2 $B$K8:$C$F$$$kLu$G$9(B. $B$=$l$r(B
|> $BL@3N$K$9$k$K$OD>8r9TNs(B  P $B$rMQ$$$F=q$-D>$9$HNI$$(B
|> $B$H$$$&$N$,;d$N?=$7>e$2$F$$$k$H$3$m$G$9(B.
|> 
|> $BF1CM$JJ}Dx<0$X$NJQ7A$G$9$+$i0lHL@-$r<:$&$3$H$O$"$j$^$;$s(B.
|> 
|> >   $B$b$&0lE@$r3NG'$7$?$$$G$9$,!"A*Dj$7$?D>8r9TNs(B P$B!"$3$N(B P$B$r(B
|> > P_1$B$H$7$^$9!#(BP_1$B$GDj$^$k9TNs&!$O0lC6$=$NH>@5DjCM$N>r7o$rK~(B
|> > $BB-$7$J$$>l9g$K$O!"$^$?<!$N(B P_2$B$"$k$$$O(B P_i$B$rC5$9$H$$$&;n9T(B
|> > $B:x8mE*$JJ}K!$r<h$C$F$h$m$7$$$G$7$g$&$+!#(B
|> 
|> $BJ,$+$jFq$$$N$G$"$l$P(B, P $B$O(B P X = e_1, P B = a e_1 + b e_2 $B$r(B
|> $BK~$?$9$b$N$r0l$D$H$C$FF0$+$5$J$$$H$*9M$(2<$5$$(B. $BC5$9$N$O(B
|>   C e_1 = \rho (a e_1 + b e_2)
|> $B$rK~$?$9BP>NH>@5DjCM9TNs(B  C $B$G$9(B. A = P^* C P $B$O<+F0E*$K(B
|> $BBP>NH>@5DjCM9TNs$G(B A X = \rho B $B$rK~$?$9$b$N$H$J$j$^$9(B.
|> 
|> # $B>e$rM}2r$5$l$?8e$G$"$l$P(B,
|> #  P X = e_1, P B = a e_1 + b e_2 $B$rK~$?$9(B
|> # P $B$r<h$jBX$($l$PB>$N2r$,8+$D$+$k$H$+(B,
|> # $B$=$l$O2r(B  C $B$r<h$jBX$($F$$$k$3$H$KB>$J$i$J$$$H$+(B,
|> # $B$3$N4X78$rMxMQ$7$F(B  C $B$N7A$rM=$a@)8B$G$-$k$H$+(B,
|> # $BOC$r?J$a$F$bNI$$$N$G$9$,(B. $B;d$NA05-;v$G$N(B  P $B$r<h$jBX$($F(B
|> # $B1>!9$NItJ,$O:9$7Ev$?$C$F$O$*K:$l2<$5$$(B.
|> -- 
|> $BDMK\@i=)(B@$B1~MQ?t3X(B.$B9bJ,;R3X2J(B.$BA!0]3XIt(B.$B5~ET9)7]A!0]Bg3X(B
|> Tsukamoto, C. : chiaki@ipc.kit.ac.jp

    $B:G8e!"(Bfj.sci.math$B$N$_$J$5$s!"$^$?59$7$/!#(B
    //////////////////////////////////////////////////////////////...
   /////////  ////          /////////// $B>O(B  $B9((B //////////////////...
  /////////  ////  /////  //////// $B@)8f%7%9%F%`65<<(B ////////////...
 /////////  ////  ////  //////$B6e=#9)6HBg3X(B  $B>pJs9)3XIt(B ////////...
/////////        ///  //// E-mail: zhang@ces.kyutech.ac.jp ///...
 ///////  ////  //  /// http://www.ces.kyutech.ac.jp/~zhang ///...
  /////  ////  /  /////////////// Tel. (0948)29-7738 ///////////...
   ///  ////          //  /////// Fax. (0948)29-7709 ////////////...
    //////////////////////////////////////////////////////////////...
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Message-ID: <50r32k$mh8@ces.ces.kyutech.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <50q4v6$5vg@sakura.kudpc.kyoto-u.ac.jp>

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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,22a531ac63328363
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From: zhang@ces.ces.kyutech.ac.jp (Hong Zhang)
Subject: Re: How to solve the LMI of symmetric matrix's semidefinite condition?
Date: 1996/09/07
Message-ID: <50r32k$mh8@ces.ces.kyutech.ac.jp>
X-Deja-AN: 180431476
references: <50q4v6$5vg@sakura.kudpc.kyoto-u.ac.jp>
organization: Dept. of CES, Kyushu Institute of Tech.,IIZUKA,Japan
reply-to: zhang@ces.ces.kyutech.ac.jp
newsgroups: fj.sci.math