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Article #13546

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

#13546
From: Hong Zhang
Date: Fri, 06 Sep 1996 00:00
63 lines
2967 bytes
from article <50mrk1$gg3@sakura.kudpc.kyoto-u.ac.jp>,
	by g52997@sakura.kudpc.kyoto-u.ac.jp (Tsukamoto, Chiaki):

|> $B9)A!Bg$NDMK\$G$9(B.

   $B$5$i$KL@3N$J8f2sEzM-Fq$&8f:B$$$^$7$?!#(B
|> 
|> $BD>8r9TNs(B  P $B$O0l0U$K$ODj$^$j$^$;$s$,(B,
|> $BJ}Dx<0$r=q$-D>$9$K$O>r7o(B  P X = e_1, P B = a e_1 + b e_2 $B$r(B
|> $BK~$?$9$b$N$r0l$D<h$C$F8GDj$9$l$PNI$/(B,
|> $BBP>NH>@5DjCM9TNs(B  A $B$NA4BN$r5a$a$k$3$H$O(B
|> $BBP>NH>@5DjCM9TNs(B  C $B$NA4BN$r5a$a$k$3$H$K5"Ce$7$^$9(B.
|> $B$J$*(B, P $B$N<h$jJ}$NITDj@-$rMxMQ$7$F(B  C $B$N7A$r$b$&>/$7@)8B$7(B,
|> $BH>@5DjCM@-$rH=Dj$7$d$9$/=PMh$?$j$9$k$H;W$$$^$9$,(B,
|> $B$=$l$O$48&5f2<$5$$(B.
|> 
|> > $B$^$?(B n $B<!85$N(B
|> > $BLdBj$K3HD%$9$k$H!">e5-$N(BMatrix$B$NCf$N(B*$B$H$3$m$NCM$OG!2?$KDj$a(B
|> > $B$k$+$K$F!"MF0W$G$O$J$$$H;W$C$F!"G!2?$G$7$g$&!#(B
|> 
|> n = 4 $B$G@5DjCM$N>r7o$G$b$N$r9M$($k$J$i$P(B
|> 
|> a b 0 0
|> b c d e
|> 0 d f g
|> 0 e g h
|> 
|> $B$G(B c, d, e, f, g, h $B$r(B (a > 0 $B$O2>Dj$7$F$*$$$F(B)
|> 
|> |a b| = a c - b^2 > 0,
|> |b c|
|> 
|> |a b 0|
|> |b c d| = (a c - b^2) e - a d^2 > 0,
|> |0 d e|
|> 
|> |a b 0 0|
|> |b c d e| > 0,
|> |0 d f g|
|> |0 e g h|
|> 
|> $B$rK~$?$9$h$&$K<h$k$3$H$,I,MW==J,>r7o$H$J$k$H$$$&0UL#$G(B
|> $B0l$D$N2rK!$K$O$J$j$^$9(B.

  $B$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

  $B$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

    //////////////////////////////////////////////////////////////...
   /////////  ////          /////////// $B>O(B  $B9((B //////////////////...
  /////////  ////  /////  //////// $B@)8f%7%9%F%`65<<(B ////////////...
 /////////  ////  ////  //////$B6e=#9)6HBg3X(B  $B>pJs9)3XIt(B ////////...
/////////        ///  //// E-mail: zhang@ces.kyutech.ac.jp ///...
 ///////  ////  //  /// http://www.ces.kyutech.ac.jp/~zhang ///...
  /////  ////  /  /////////////// Tel. (0948)29-7738 ///////////...
   ///  ////          //  /////// Fax. (0948)29-7709 ////////////...
    //////////////////////////////////////////////////////////////...
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Message-ID: <50op6f$j53@ces.ces.kyutech.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <50mrk1$gg3@sakura.kudpc.kyoto-u.ac.jp>

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X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,22a531ac63328363
X-Google-Attributes: gidf4956,public
From: zhang@ces.ces.kyutech.ac.jp (Hong Zhang)
Subject: Re: How to solve the LMI of symmetric matrix's semidefinite condition?
Date: 1996/09/06
Message-ID: <50op6f$j53@ces.ces.kyutech.ac.jp>
X-Deja-AN: 179533722
references: <50mrk1$gg3@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