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$@ ;)&8 *-)'(0< /&=/)4+11<+>1-3+1(@ &7'+,+$@L)/@ 2-2 '+K+1(@ /&&)4+)/)4.LC+%& 24-,'-)1&%& .'-41+1(@.;1;;;10. x+)&, &='-)1&8 ()+'-0(( 7&>4&$@+) 1-8)( /&=/)4+11<8 4+2)&', /&&)4+)/)4.LC(8 &,1&2'-)1&*. /&=/)4+11&*. >1-3+1(L ,(-%&1-$(>('.+*&8 *-)'(0<A 2 Mn , +/$( (>4+/)1& ,&/)-)&31& 6&'&K++ 7'(=$(A+1(+ b 2 /&=/)4+11&*.>1-3+1(L .% 1 ($ >% %6). ( A 2 Mn ' ei , i = 1 : : : n :Aei = iei , (ei ej ) = ij , m , m = 1 2 : : : n . ( b m 6= m { " m :m ; b m max (1)b m = q < 1:i=12:::n i ; i=m6* x(0) 2 Cn , (x(0) em ) 6= 0 , x(k+1) ; " (A ; b mI )x(k+1) = x(k)(k+1)e(mk+1) = kxx(k+1) k k = 0 1 : : :(2) em ( ' ):e(mk) ! ei' em k ! 1.. x10.
& &+ &$131( ei' { , ' 1 ). ( & k0 > 0 , k k0 ke(mk) ; ei'emk Cqk(3) C k .:"#&. 9&/2&$:2. 4+2)&'- e1 : : : en &='->.L) =->(/ 4 C n , )&nx(0) = P ciei , 7'(3+* 7& ./$&4(L cm = (x(0) em) 6= 0. 9&/2&$:2.i=1x(k+1) = (A ; b mI ) 1x(k) ;)&x(k+1) = (A ; b mI ) k x(0) :-2 2-2 /&=/)4+11<+ >1-3+1(@ *-)'(0< A ; b mI '-41< i ; b m , i = 1 2 : : : n ,)& /&=/)4+11<+ >1-3+1(@ *-)'(0< (A ; b mI ) 1 +/): (i ; b m ) 1 , i = 1 2 : : : n ,- *-)'(0< (A ; b mI ) 1 | (i ; b m ) k , i = 1 2 : : : n .
$+,&4-)+$:1&,nnXXci eix(k) = (A ; b mI ) k ciei =bi=1i=1 (i ; m )k01!kn cXBBcmm ; b m CiCA=e+emibc(m ; b m )k @;imi=1 m;;;;;;i=m6 /($. &')&1&'*('&4-11&/)( =->(/- feig01!2knbkx(k)k2 = (x(k) x(k)) = (m ;1b m)2k BB@jcmj2 + X jcij2 mi ;;bmm CCA :i=1i=mn /($.
(1) ( '-4+1/)4- kx(0) k2 = P jcij2 7&$.3-+*6i=1($(jcmj kx(k)k jcmj 1 + kx(0)k2 q2k !1=2jcmj2(m ; b m)k(m ; b m )k(0) k2 ! 1=2kxjcmj 1 11 + jc j2 q2k(m ; b m)k kx(k)km;<3(/$(*!cm1 ; cm ex(k) ; cm e =kx(k)k jcmj m (m ; bm)k kx(k)k jcmj mnb m !kXcc1imm;+ kx(k) k:e(m ; b m)k cm i i ; b mi=1i=m6.. x10. & &+ &$132 /($. (1), (2) ( '-4+1/)4 kei k = 1, i = 1 2 : : : n , &=&>1-3(4 ei' = cm =jcmj ,1-6&,(* (k) i' 0 kx(0) k2 2k !em ; e em @1 ; 1 + jc j2 q;m-2 2-2)&nXi=11=2 1nA + X jcij qk :i=1 jcm ji=m6X!1=2 pnp2jcij n jcij = n kx(0)ki=1 (k) i' 0 kx(0) k2 2k !em ; e em @1 ; 1 + jc j2 q1=2 1A + pn kx k qkjcmjm /($.
(1) 1-8,+)/@ k0 > 0, )-2&+, 3)& ,$@ 4/+6 k k0 4<7&$1+1& kx(0) k2 q2k < 1. &%,- (1 ; ) 1=2 1 ; =2 ( 1 ; (1 ; ) 1=2 =2 1=2=2.jcmj29&;)&*. ,$@ 4/+6 k k0 /7'-4+,$(4& 1+'-4+1/)4& (k) i' kx(0) kpem ; e em jc j (1=2 + n) qk :m(0);;;F)& 1+'-4+1/)4& @4$@+)/@ )'+=.+*&8 &0+12&8 (3)... 133- .-$$ /0-$1. -)'(31<+ 1&'*<. 9&,3(1+1<+ *-)'(31<+ 1&'*<.2.
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
LU -'->$&A+1(+.9. $%&'()* 7&/)'&+1(@ LU -'->$&A+1(@. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.10. '()+'(8 &/.C+/)4(*&/)( *+)&,- !-.//-.11. +)&, !-.//- ,$@ $+1)&31<6 *-)'(0. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.12. $%&'()* 7&/)'&+1(@ LU -'->$&A+1(@ ,$@ )'+6,(-%&1-$:1<6 *-)'(0.0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.
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
+)&, &$+02&%& (24-,'-)1&%& 2&'1@) '+K+1(@ /(/)+* $(1+81<6 .'-41+1(8. '%-1(>-0(@ 7'&0+//- 4<3(/$+1(8 ( 6'-1+1(@ *-)'(0 4 7-*@)( F.0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.20. +)&, &')&%&1-$(>-0(( '+K+1(@ /(/)+* $(1+81<6 .'-41+1(8. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.21. -)'(0- ;$+*+1)-'1&%& 4'-C+1(@ ( ++ /4&8/)4- (%+&*+)'(3+/2(8 /*</$,>-)'-)< 1- 4<3(/$+1(+ 7'&(>4+,+1(8 1- 4+2)&' ( *-)'(0.).22. +)&, 4'-C+1(8 '+K+1(@ /(/)+* $(1+81<6 .'-41+1(8.
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
,(1/)4+11&/): '->$&A+1(@. 7&/&=< 6'-1+1(@ *-)'(0 Q ( R 4 7-*@)( F.0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8, 1+&=6&,(*<6 ,$@ 7&/)'&+1(@QR -'->$&A+1(@.27. 9'(4+,+1(+ *-)'(0< 2 7&3)( )'+.%&$:1&*. 4(,. .1()-'1<* 7&,&=(+* *+)&,&* 4'-C+1(8. /.C+/)4(*&/):. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.28. 9'(4+,+1(+ /(**+)'(31&8 *-)'(0< 2 )'+6,(-%&1-$:1&*. 4(,. .1()-'1<*7&,&=(+* *+)&,&* 4'-C+1(8. /.C+/)4(*&/):.
0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8....99:: ;<9.4 =13529. 9'(4+,+1(+ *-)'(0< 2 7&3)( )'+.%&$:1&*. 4(,. .1()-'1<* 7&,&=(+* *+)&,&* &)'-A+1(8. /.C+/)4(*&/):. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.30. 9'(4+,+1(+ /(**+)'(31&8 *-)'(0< 2 )'+6,(-%&1-$:1&*. 4(,. .1()-'1<*7&,&=(+* *+)&,&* &)'-A+1(8. /.C+/)4(*&/):. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8.31.
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
9'+&='->&4-1(+ ;$+*+1)-'1&%& 4'-C+1(@, (/7&$:>.+*&+ 4 *+)&,+ 4'-C+1(82&=(. (, 5&'*.$, &=+/7+3(4-LC(8 *+1:K++ 1-2&7$+1(+ 4<3(/$()+$:1&8 7&%'+K1&/)(.36. )'-)+%(( 4<=&'- &3+'+,1&%& &=1.$@+*&%& ;$+*+1)- 4 *+)&,+ 2&=(. 0+12- /2&'&/)( /6&,(*&/)( 4 /$.3-+ &=1.$+1(@ *-2/(*-$:1&%& 7& *&,.$L 41+,(-%&1-$:1&%& ;$+*+1)-. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8 1- &,(1K-% -$%&'()*- ,$@ 2-A,&8 (> /)'-)+%(8.37. <3(/$+1(+ k -%& 7& 4+$(3(1+ /&=/)4+11&%& >1-3+1(@ *+)&,&* =(/+20((.0+12- 2&$(3+/)4- ()+'-0(8.
7&/&=< 4<3(/$+1(@ 3(/$- 7+'+*+1 >1-2- 47&/$+,&4-)+$:1&/)( %$-41<6 *(1&'&4. '%-1(>-0(@ 7'&0+//- 4<3(/$+1(8,$@ 7'+,&)4'-C+1(@ 7+'+7&$1+1(@ ($( 7&)+'( )&31&/)(.38. <3(/$+1(+ 4/+6 /&=/)4+11<6 >1-3+1(8 *-)'(0< 1- >-,-11&* (1)+'4-$+*+)&,&* =(/+20((. 0+12- 2&$(3+/)4- ()+'-0(8. 7&/&=< 4<3(/$+1(@ 3(/$- 7+'+*+1 >1-2- 4 7&/$+,&4-)+$:1&/)( %$-41<6 *(1&'&4. '%-1(>-0(@7'&0+//- 4<3(/$+1(8 ,$@ 7'+,&)4'-C+1(@ 7+'+7&$1+1(@ ($( 7&)+'( )&31&/)(.39.
+&'+*- & LR -'->$&A+1((. LR --$%&'()* 7&(/2- /&=/)4+11<6 >1-3+1(8,+%& &/.C+/)4(*&/):. &/)-)&31<+ ./$&4(@ /6&,(*&/)( (=+> ,&2->-)+$:/)4-).40. $%&'()* 7&/)'&+1(@ LR -'->$&A+1(@. &6'-1+1(+ 7&3)( )'+.%&$:1&%& 4(,- *-)'(0< 4 LR --$%&'()*+ 1-6&A,+1(@ /&=/)4+11<6 >1-3+1(8....99:: ;<9.4 =13641.
$%&'()* 7&/)'&+1(@ LR -'->$&A+1(@ ,$@ 7&3)( )'+.%&$:1&8 *-)'(0<.-/3+)1<+ 5&'*.$< LR --$%&'()*- 1-6&A,+1(@ /&=/)4+11<6 >1-3+1(8 ,$@7&3)( )'+.%&$:1&8 *-)'(0<. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8 1&,(1 K-% -$%&'()*-.42. "/2&'+1(+ /6&,(*&/)( LR --$%&'()*- / 7&*&C:L (/3+'7<4-1(@ *-)'(0<( /,4(%&4 (=+> ,&2->-)+$:/)4-). 9'(*+' 4<=&'- /,4(%- ( (/3+'7<4-1(@ *-)'(0<.43. +&'+*- & '->$&A+1(( &$+02&%&, (/7&$:>.+*&* 4 *+)&,+ &$+02&%& 7&(/2- /&=/)4+11<6 >1-3+1(8 /(**+)'(31&8 *-)'(0<.
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
-/3+)1<+ 5&'*.$< *+)&,- &$+02&%& 7&(/2- /&=/)4+11<6 >1-3+1(8 ,$@ )'+6,(-%&1-$:1&8 *-)'(0<. 0+12- 3(/$- -'(5*+)(3+/2(6 &7+'-0(8 1- &,(1 K-% -$%&'()*-.46. "/2&'+1(+ /6&,(*&/)( *+)&,- &$+02&%& 7&(/2- /&=/)4+11<6 >1-3+1(8 /7&*&C:L (/3+'7<4-1(@ *-)'(0< ( /,4(%&4 (=+> ,&2->-)+$:/)4-). 9'(*+'4<=&'- /,4(%- ( (/3+'7<4-1(@ *-)'(0<.47. QR --$%&'()* 7&(/2- /&=/)4+11<6 >1-3+1(8, +%& &/.C+/)4(*&/):.
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
9'-2)(2.* 7& -$%+='+. 9&, '+,. .. -64-$&4-, .. &/)'(2(1-. >,.-4&!", 1983.2. D.9. ->*</$&4, .. C+12&. 9'-2)(2.* 7& 4<3(/$()+$:1<* *+)&,-* -$%+='<. >,.-4& !", 1988.3. .. -64-$&4, .9. G(,2&4, !.. &=+$:2&4. (/$+11<+ *+)&,<. ., "-.2-", 1987.4.
.. ^-,,++4, .. ^-,,++4-. <3(/$()+$:1<+ *+)&,< $(1+81&8 -$%+='<,1963.5. A.. "($2(1/&1. $%+='-(3+/2-@ 7'&=$+*- /&=/)4+11<6 >1-3+1(8. ., "-.2-", 1970.6. . &'1, . A&1/&1. -)'(31<8 -1-$(>. ., "('", 1989.7. .. -*-'/2(8, .. !.$(1. (/$+11<+ *+)&,<. ., "-.2-", 1989.8. . 9(//-1+02(. +61&$&%(@ '->'+A+11<6 *-)'(0. ., "('", 1988...>; ?9<9.