21
FACULDADE ANHANGUERA DE CUIABÁ  ENGENHARIA CIVIL CARLOS EDUARDO CORREIA DELAMONICA – RA : 1569228993 DEZYRE MIKAELA DA SILVA ALBUQUERQUE – R A : 672333545 ELIZALDO BARBOSA – RA: 1590825455 MAYCON DOS SANOS !ESUS – RA : 1572197974 VANESSA RE"INA DE #AULA – RA 86912 49570 AIVIDADE SU#ERVISIONADA CALCULO NUM$RICO %EA#A 1&2&3' CUIABÁ-MT JUNHO/2015 CARLOS EDUARDO CORREIA DELAMONICA – RA : 1569228993 DEZYRE MIKAELA DA SILVA ALBUQUERQUE – R A : 672333545 ELIZALDO BARBOSA – RA: 1590825455

elizaldo

Embed Size (px)

Citation preview

Page 1: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 1/21

FACULDADE ANHANGUERA DE CUIABÁ

  ENGENHARIA CIVIL

CARLOS EDUARDO CORREIA DELAMONICA – RA :1569228993

DEZYRE MIKAELA DA SILVA ALBUQUERQUE – RA : 672333545

ELIZALDO BARBOSA – RA: 1590825455

MAYCON DOS SANOS !ESUS – RA : 1572197974

VANESSA RE"INA DE #AULA – RA 8691249570

AIVIDADE SU#ERVISIONADA

CALCULO NUM$RICO

%EA#A 1&2&3'

CUIABÁ-MT

JUNHO/2015

CARLOS EDUARDO CORREIA DELAMONICA – RA : 1569228993

DEZYRE MIKAELA DA SILVA ALBUQUERQUE – RA : 672333545

ELIZALDO BARBOSA – RA: 1590825455

Page 2: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 2/21

MAYCON DOS SANOS !ESUS – RA : 1572197974

VANESSA RE"INA DE #AULA – RA 8691249570

CÁLCULO NUMÉRICO

%EA#A 1&2&3'

  Trabal! a"r#$#%&a'! a! ()r$! '#*E%+#%ar,a(,,l 'a .a()l'a'# a%a%+)#ra '# C),ab "ara!b&#%! '# %!&a "ar(,al # (!%#(,#%&! #

 ba$# '! #$&)'! ,$&! # $ala ,%&#+ra'! a

AT34*'a ',$(,"l,%a '# (al()l! %)r,(!*4!b!r,#%&a! '! "r!.#$$!r6  E'$!% B#%#',&!A%&)%#$ A%+#l! 'a 4,la6

CUIABÁ-MT

ABRIL/2015

Conteúdo

INTRODU7AO..................................................................................................4

D#$a.,!............................................................................................................. 5

ETA3A 1 8&#"! "ara r#al,9a!: 05 !ra$;................................................................7CÁLCULO NUMÉRICO......................................................................................7

Page 3: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 3/21

3a$$! 2 8E<),"#;..................................................................................................8

26 D#$a.,! B.................................................................................................... 8

4!l)!:......................................................................................................9

=6 D#$a.,! =.................................................................................................... 9

4!l)!...................................................................................................... 9

3a$$! = 8 #<),"# ;.............................................................................................9

16D#$a.,! A.....................................................................................................9

26D#$a.,! B.....................................................................................................9

=6D#$a.,! (..................................................................................................... 9

E&a"a > 2......................................................................................................... 10

A)la$-&#a$: 4,$&#a$ '# N)#ra! # Err!$6...........................................................10

3a$$! 1........................................................................................................... 103a$$! 2........................................................................................................... 11

3a$$! = 8E<),"#;................................................................................................11

ETA3A =:........................................................................................................ 12

4OLU7ÁO NUMÉRICA DE 4I4TEMA LINEARE4..................................................12

163a$$!........................................................................................................... 13

C!%(#,&!$ ,%&r!')&?r,!$ '# $,$&#a$ l,%#ar#$.............................................................13

3a$$! 2........................................................................................................... 14

3a$$! =........................................................................................................... 16

3a$$! @........................................................................................................... 17

RELAORIO =:4!l)#$ %)r,(a$ '# $,$&#a '# #<)a#$ l,%#ar#$-"ar&#1.......................17

CONCLU4O..................................................................................................18

REFERENCIA BIBIOGRAFICA...........................................................................19

Page 4: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 4/21

INTRODU7AO

 N#$&# &rabal! a"r#$#%&ar#!$ )a &#!r,a '! <)# (l()l! %)r,(! <)# $#ra"r#$#%&a'! # ) br## &#&! # ) "!)(! (!! #la )$a'a %a "ra&,(a* !) $#a* #l+#bra l,%#ar <)# #$&a r#"r#$#%&a'a # ##r((,!$ "r!"!$&! "#l! "r!.#$$!r6

  O !b#&,! '#$&# &rabal! '#$#%!l#r # a"r,!rar %!$$!$ (!%#(,#%&!$ (!a r#la! a (!%(#,&!$ # "r,%(",!$ +#ra,$ '! (al()l! %)r,(!6 O '#$a.,! '#$&# &rabal!'#$#%!l#r a$ #&a"a$ = <)# $#r ! (!"r,#%&! '#$(!br,r ! (?',+! '# barra$ l,%#ar

 "al%'r!! (! =@ barra$ <)# (a!) a a&#%! 'a ,"!r&a'!ra *V#%'!)%'!6

  3ara ,$&! &#r#!$ <)# r#al,9ar # (!%(l),r $#&# &ar#.a$ <)# a"!$ '#,'a#%&#

(!%(l)'!$ &#r#!$ <)# a$$!(,ar a r#$"!$&a a ) %#r!: 0 !) 16 E$$#$ %#r!$

Page 5: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 5/21

(!l!(a'!$ la'! a la'! # %a !r'# '# r#al,9a! 'a$ #&a"a$ .!r%#(#r! !$ '#9#$$#&#

 "r,#,r!$ al+ar,$!$ 'a #$<)#r'a "ara a ',r#,&a <)# ,r! (!"!r ! (?',+! '# barra$

l,%#ar6

A A&,,'a'# 3r&,(a 4)"#r,$,!%a'a 8AT34; ) "r!(#',#%&! #&!'!l?+,(! '##%$,%!-a"r#%',9a+# '#$#%!l,'! "!r #,! '# #&a"a$* a(!"a%a'a$ "#l! "r!.#$$!r* #<)# &# "!r !b#&,!$:

Fa!r#(#r a a)&!a"r#%',9a+# '! al)%!6

E$&,)lar a (!rr#$"!%$ab,l,'a'# '! al)%! "#l! $#) a"r#%',9a'!6

3r!!#r ! #$&)'!* a (!%,%(,a # ! &rabal! # +r)"!6

 A),l,ar %! '#$#%!l,#%&! 'a$ (!"#&%(,a$ r#<)#r,'a$ "ara ! ##r((,! "r!.,$$,!%al6

Page 6: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 6/21

 3r!!#r a a"l,(a! 'a &#!r,a %a $!l)! '# $,&)a#$ <)# $,)la a r#al,'a'#6

O.#r#(#r ',.#r#%(,a'!$ ab,#%&#$ '# a"r#%',9a+#6

3ara a&,%+,r #$&#$ !b#&,!$* a AT34 "r!"# ) '#$a.,! # ,%',(a !$ "a$$!$ a $#r#

 "#r(!rr,'!$ a! l!%+! '! $##$&r# "ara a $)a $!l)!6 A"r!#,&# #$&a !"!r&)%,'a'# '##$&)'ar # a"r#%'#r (! '#$a.,!$ 'a ,'a "r!.,$$,!%al6

D()*+,-

O (?',+! '# barra$* (!%&,'! %a a,!r "ar&# '!$ "r!')&!$ ,%')$&r,al,9a'!$* (!%$,$&#%) (!%)%&! '# r,a$ barra$ <)# "!'# #$&ar "r##%(,'a$ (! a (!r #$()ra !) %!6

)a%'! ) l#,&!r ?"&,(!* &ab (aa'! '# $(a%%#r$* "a$$a $!br# #$$a$ barra$* al#,&)ra '# )a barra (lara (!%#r&,'a %! %#r! 0 89#r!; # a '# )a barra #$()ra* %!%#r! 16

Ob$#rar %a .,+)ra a! la'!* ) ##"l! $,"l,.,(a'! '# ) (?',+! # )$,$&#a '# (?',+! l,%#ar (! =1 barra$6

4# ! l#,&!r ?"&,(! .!r "a$$a'! 'a #$<)#r'a "ara a ',r#,&a ,r l#r:01010001101010011101010001101016 4# ! l#,&!r ?"&,(! .!r "a$$a'! 'a ',r#,&a "ara a#$<)#r'a ,r l#r: 10101100010101110010101100010106

Mar(!$ "r!"r,#&r,! 'a #"r#$a '# ,"!r&a! (aa'a V#%'!)%'!6

A%!$ a&r$* ,$a%'! a,$ #.,(,%(,a %a l!(al,9a! '!$ (!%&,%#r#$ # ',,%),!'!$ #rr!$ +#ra'!$ "!r ,%&#r.#r%(,a )a%a* Mar(!$ (!%&ra&!) !$ $#r,!$ '# )a#"r#$a (! #"#r&,$# %! '#$#%!l,#%&! '# $!l)#$ ,%&#l,+#%&#$ "ara l!+$&,(a

 "!r&)r,a # r#(,%&!$ al.a%'#+a'!$6

O$ (?',+!$ '# barra$ l,%#ar#$* b,',#%$,!%a,$ # !)&ra$ &#(%!l!+,a$* (!! G3484,$&#a '# 3!$,(,!%a#%&! Gl!bal* # "!r&)+)$;* "a$$ara a $#r )&,l,9a'!$ "#la

,"!r&a'!ra '#$'# #%&!* (!! )a 'a$ .!ra$ '# l!(al,9a! '# "r!')&!$* )%,'a'#$l!+$&,(a$* r#+,$&r! '# (!%&,%#r#$* '!()#%&!$* $#r,!$ # (ar+a$6 E$$a &#(%!l!+,a* $#','a* &r!)# a)&!a! "ara a a,!r,a '!$ "r!(#$$!$* +#ra%'! #.,(,%(,a* a,!r(!%&r!l# # (!%.,ab,l,'a'# "ara a #"r#$a6

 N! $,$&#a '# (?',+! '# barra$ l,%#ar* "ara !r+a%,9ar ! "r!(#$$! '# l#,&)ra ?"&,(a'# (a'a (?',+!* '##-$# l#ar # (!%$,'#ra! <)# al+)%$ '#l#$ "!'# &#r l#,&)ra 'a#$<)#r'a "ara a ',r#,&a ,+)al K 'a ',r#,&a "ara a #$<)#r'a6 3ara ##"l,.,(ar*a"r#$#%&a!$ ! (?',+!: 010010001111000100106 T#!$ a<), ) ##"l! '# )(?',+! '# barra$ l,%#ar "al%'r!!6

Page 7: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 7/21

C)r,!$a#%&#* a l,$&a+# '# ) %!! l!&# '# (!%&,%#r#$ 'a #"r#$a '# Mar(!$*r#(#%&##%&# '#$#bar(a'! %! "!r&! '# 4a%&!$* a$$!(,aa ) (?',+! l,%#ar "al%'r!!a ) '!$ (!%&,%#r#$6

O '#$a.,! "r!"!$&! %#$&# (a'#r%! '# a&,,'a'#$ : '#$()bra ! (?',+! l,%#ar

 "al%'r!! (! =@ barra$ <)# (a!) a a&#%! '# Mar(!$ "#la $)a #(#%&r,(,'a'#6

3ara &a%&!* $#&# '#$a.,!$ $! "r!"!$&!$6 Ca'a '#$a.,!* a"?$ $#r '#,'a#%&#r#al,9a'!* '##r $#r a$$!(,a'! a ) %#r!: 0 !) 16 E$$#$ %#r!$* <)a%'! (!l!(a'!$la'! a la'! # %a !r'# '# r#al,9a! 'a$ #&a"a$* .!r%#(#r! !$ '#9#$$#&# "r,#,r!$al+ar,$!$ 8'a #$<)#r'a "ara a ',r#,&a; <)# ,r! (!"!r ! (?',+! '# barra$ l,%#ar

 "al%'r!! <)# .!, a$$!(,a'! a ) '!$ (!%&,%#r#$ r#(#%&##%&# '#$#bar(a'! %! "!r&! '# 4a%&! "#la ,"!r&a'!ra V#%'!)%'!6

EA#A 1 %.(/- ** (*,*-: 05 -*)' A)la$-&#a$: C!%(#,&!$ # 3r,%(",!$ G#ra,$ '# Cl()l! N)r,(!6 E$&a #&a"a

,"!r&a%&# "ara <)# !( .,#* '# .!ra "r&,(a* !$ (!%(#,&!$ b$,(!$ '# l+#bra l,%#ar<)# ,r! $#r,r '# $)"!r&# "ara a (!"r##%$! '!$ &!'!$ %)r,(!$ &rabala'!$ "#l!

 "r!.#$$!r 'a ',$(,"l,%a # (a'a a)la &#a 'a ',$(,"l,%a '# Cl()l! N)r,(!6

3ara r#al,9-la* '## $#r $#+),'!$ !$ "a$$!$ '#$(r,&!$6

3a$$! 1 8E<),"#; Fa9#r a$ a&,,'a'#$ a"r#$#%&a'a$ a $#+),r6

16 L#r a&#%&a#%&# ! (a"&)l! '! l,r!-&#&! 8FRANCO* N#,'# M6 B6 Cl()l! N)r,(!6 1 #'6 4! 3a)l!: 3#ar$!% > 3r#%&,(# Hall* 200; <)# '#$(r## !$ (!%(#,&!$ #

Page 8: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 8/21

 "r,%(",!$ +#ra,$ '# (l()l! %)r,(!6 3#$<),$ar &ab #: l,r!$ ','&,(!$ '! E%$,%!4)"#r,!r* %a I%&#r%#& # # !)&ra$ .!%&#$ '# l,r# #$(!la* ,%.!ra#$ l,+a'a$ a! #$&)'!# )&,l,9a! 'a l+#bra l,%#ar # (l()l! %)r,(!6

26 Elab!rar ) &#&! ',$$#r&a&,!* (!%&#%'! a$ "r,%(,"a,$ ,%.!ra#$ #%(!%&ra'a$

(! a "#$<),$a r#al,9a'a %! "a$$! 16 E$&a "#$<),$a $#r ,"r#$(,%'#l "ara a(!"r##%$! # r#al,9a! '!$ "r?,!$ "a$$!$6

CLCULO NUM$RICO3!'#!$ r#$),r (l()l! %)r,(! (!! )a &(%,(a '# $!l)(,!%ar "r!bl#a$

)$a%'! (!")&a'!r#$6 U&,l,9a%'! '# &!'!$ %)r,(!$ ! (l()l! %)r,(! !b& )a$!l)! a(#,&#l* !) $#a* b# "r?,a 'a ,'#al '# "r!bl#a$ '# l+#bra l,%#ar #

l+#bra %! l,%#ar6

E$$a$ &(%,(a$ '! (l()l! %)r,(! $! )&,l,9a'a$ "r,%(,"al#%&# # "r!bl#a$!%'# %! a"r#$#%&a $!l)#$ #a&a$* #$&#$ &a,$ "r!bl#a$ "!'# $#r r#$!l,'!$a%al,&,(a#%&#* "!r#* "!'# $# &!r%ar ,"!$$#l '# $!l)(,!%ar '#,'! a! $#) &aa%!63!r #$$# !&,! )&,l,9a-$# a a"r!,a! <)# "!'# $#r a(#,&#l %a $,&)a!6 N!$

 "r!bl#a$ r#a,$* !$ 'a'!$ $! #','a$* "!r &a%&! %! $! #a&!$6 Ua #','a .$,(a %! (!%$,'#ra'! ) %)#r! # $, ) ,%&#ral!* "#la "r?"r,a ,"r#(,$! 'a$ #','a$*%#$&# (a$! &rabala-$# (! .,+)ra '# #rr!6

M*) -/- ()-( / -;(/* (* .,,*<=- *) .><,*) =- *-</>,-???

O "r,#,r! "a$$! "ara $# r#$!l#r ) "r!bl#a )&,l,9a%'! a$ &(%,(a$ '! (l()l!%)r,(! definir o problema* '#"!,$ !( '##r descobrir um método matemático

 para representar o problema real # "!r ., !( '## Calcular uma solução numérica

do problema originado da modelagem matemática6 E$&# l&,! "a$$! '## $#r ',,','!# &r$ #&a"a$:

16 I%',(ar )a .!ra %)r,(a '# $!l)! # (!%$&r),r ) al+!r,&!* !) $#a*

'#$(r##r ) (!%)%&! '# (!a%'!$ <)# r#$)l&ara # )a $#<)%(,a .,%,&a '#(!,$a$/a(!%&#(,#%&!$6

26 R##$(r##r ! al+!r,&! # ) (?',+! !) )a l,%+)a+# <)# "!$$a $#r,%&#r"r#&a'a "#l! (!")&a'!r6

=6 M!%&ar ! (?',+! # ) (!")&a'!r # ##()&-l! a& <)# $#a #l,,%a'!$ !$#rr!$ # "!$$a $#r !b&,'!$ !$ r#$)l&a'!$6

Page 9: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 9/21

#*))- 2 %E@,('16 D#$a.,! A N!$ +r.,(!$ a $#+),r* a"r#$#%&a'a )a ,%&#r"r#&a! +#!&r,(a 'a

'#"#%'%(,a # ,%'#"#%'%(,a l,%#ar '# '!,$ # &r$ #&!r#$ %!R

D# a(!r'! (! !$ +r.,(!$ a%&#r,!r#$* a.,ra-$#:

I > !$ #&!r#$ 1 # 2 a"r#$#%&a'!$ %! +r.,(! 8a; $! LI 8l,%#ar#%&# ,%'#"#%'#%&#$;

II > !$ #&!r#$ 1 2 * # = a"r#$#%&a'!$ %! +r.,(! 8b; $! LI

III > !$ #&!r#$ 1 2 * # = a"r#$#%&a'!$ %! +r.,(! 8(; $! LD 8l,%#ar#%&#'#"#%'#%&#$;

 R: I errado

  II correto

  III errado

2 D()*+,- BDa'!$ !$ #&!r#$ ) P 8* @ Q1; r # P 8 = *10 11; r * "!'#!$ a.,rar <)# ) r # r $!l,%#ar#%&# ,%'#"#%'#%&#$6

S--:

@ =S 09 P 0

L1 L= @

10S 09 P 0

@ =S P 0

@SP0

0 P 0

- 11S 09 P 0

Page 10: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 10/21

-@ @@S P 0

P 0

P 0

P 0

3 D()*+,- 34#%'! W1 P 8=*-=*@; # W2 P 8-1*2*0; * a &r,"la (!!r'#%a'a '# W P2W1 > =W2 %a ba$# E 8X*-12*Y;

S--28=*-=*@; -=8-1*2*0;

8Z*-Z*Y; 8=*-Z*0;

8X*-12*Y;

#*))- 3 % (@,( 'R#$!l#r !$ '#$a.,!$ a"r#$#%&a'!$ %! '#$a.,! A*B # C* )+a%'! a$ a.,ra#$

a"r#$#%&a'a$ (! (#r&a !) #rra'a6 O$ (l()l!$ r#al,9a'!$ "ara &al )l+a#%&! '## $#r'#,'a#%&# r#+,$&ra'!$6

1D()*+,- A N#r! #%(!%&ra'! .!,: 1

2D()*+,- B N#r! #%(!%&ra'! .!,: 0

3D()*+,-  N#r! #%(!%&ra'! .!,: 1

Page 11: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 11/21

E.** – 2

A)la$-&#a$: 4,$&#a$ '# N)#ra! # Err!$6

E$&a #&a"a ,"!r&a%&# "ara <)# !( #%&#%'a* '# .!ra "r&,(a* ! .a&! '# <)# !

C!%)%&! '!$ %#r!$ r#"r#$#%&#,$ # <)al<)#r <),%a .,%,&!* ,$&! * %!

 "!$$#l r#"r#$#%&ar # )a <),%a &!'!$ !$ %#r!$ '# ) 'a'! ,%&#ral! [a* b\6

3ara r#al,9-la* '## $#r $#+),'!$ !$ "a$$!$ '#$(r,&!$6

#*))- 1

16 L#r a&#%&a#%&# ! (a"&)l! '! l,r!-&#&! 8FRANCO* N#,'# M6 B6 Cl()l! N)r,(!6

1 #'6 4! 3a)l!: 3#ar$!% > 3r#%&,(# Hall* 200; <)# '#$(r## !$ (!%(#,&!$ '# a%l,$# '#

arr#'!%'a#%&! # "!%&! .l)&)a%&#6 3#$<),$ar &ab #: l,r!$ ','&,(!$ '! E%$,%!

4)"#r,!r* %a I%&#r%#& # # !)&ra$ .!%&#$ '# l,r# #$(!la* ,%.!ra#$ l,+a'a$ a! #$&)'!

# )&,l,9a! 'a &#!r,a '# #rr!$6 4)+#$&! '# l#,&)ra '! a&#r,al (!"l##%&ar:

] CULMINATO6 J!$ Alb#r&!6 Cl()l! N)r,(!6 D,$"!%#l #:6 A(#$$! #: 1X abr6 201=6

26 Ob$#rar !$ '!,$ (a$!$ a"r#$#%&a'!$ aba,!:

8a; Ca$! A

Ua "r!.#$$!ra '# a&#&,(a 'a 1 $r,# '! #%$,%! ',! "#',) a &r$ al)%!$'a (la$$# <)# (al()la$$# a r#a '# )a (,r()%.#r%(,a '# ra,! ,+)al a 120 #&r!$6 O$

$#+),%&#$ al!r#$ .!ra !b&,'!$* r#$"#(&,a#%&#* "#l!$ al)%!$ J!!* 3#'r! # Mar,a:

@5621Z ^ * @562=X*0@ ^ # @562=Y*X=@21Z ^ 6

8b; Ca$! B

Mar(#l! !b&## a $#+),%&# &ab#la a"?$ ! (l()l! '!$ $!a&?r,!$:

=6 C!%$,'#rar !$ (a$!$ A # B a"r#$#%&a'!$ a%&#r,!r#%&# # r#$"!%'a:

Page 12: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 12/21

3!r <)# .!ra #%(!%&ra'!$ &r$ al!r#$ ',.#r#%&#$ "ara ! (a$! 8A;* (!%$,'#ra%'!

<)#

 N! !)# #rr! al+) "!r "ar&# '!$ al)%!$ %a )&,l,9a! 'a .?r)la 'a r#a '# )a

C,r()%.#r%(,a # %# %a $)b$&,&),! '! al!r '! ra,!* %a #$a_

)a%'! (!"ara'!$* #!$ )a ',.#r#%a %!$ al!r#$ !b&,'!$ %!$ (l()l!$ '!$

4!a&?r,!$ )&,l,9a%'! (a'a )a 'a$ .#rra#%&a$6 A <)# $# '## #$$a ',.#r#%a

a"r#$#%&a'a %! (a$! B_

#*))- 2

L#r ! '#$a.,! "r!"!$&!:

 N)a <),%a '# (al()lar ()! $,$&#a '# r#"r#$#%&a! )&,l,9a'! &# ba$# 10

5 '+,&!$ %a a%&,$$a # #"!#%&# %! ,%&#ral! [− Z* Z]* "!'# $# a.,rar <)#:

I > ! #%!r # ! a,!r %#r! # ?')l! %#$&a r#"r#$#%&a! $! 'a'!$ '# .!raR#$"#(&,a "!r: 0*110 -Z # 0*XXXXX10Z

II > )$a%'! ! arr#'!%'a#%&!* ! %#r! 12=@5Z $#r r#"r#$#%&a'! "!r 0*12=@Z10Z #

$# .!r )$a'! ! &r)%(a#%&!* ! #$! %#r! $#r r#"r#$#%&a'! "!r 0*12=@510Z

III > $# P @ # S P @5200* ! r#$)l&a'! '# S $#r 0*@ 10Y6

3a$$! = 8E<),"#;

R#$!l#r ! '#$a.,! a"r#$#%&a'! %! "a$$! 2* )l+a%'! a$ a.,ra#$ a"r#$#%&a'a$

(!! (#r&a O) #rra'a6 O$ (l()l!$ r#al,9a'!$ "ara &al )l+a#%&! '## $#r 

'#,'a#%&# r#+,$&ra'!$ "ara "!$&#r,!r#%&# $#r# a"r#$#%&a'!$ a! "r!.#$$!r 'a

',$(,"l,%a6

Page 13: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 13/21

A$$!(,ar ! %#r! 0* $# a a.,ra! I #$&,#r (#r&a6

A$$!(,ar ! %#r! 1* $# a a.,ra! I #$&,#r #rra'a6 P 0 P 0*XXXXX10Z

A$$!(,ar ! %#r! 0* $# a a.,ra! II #$&,#r (#r&a6

A$$!(,ar ! %#r! 1* $# a a.,ra! II #$&,#r #rra'a6 P 0 P 0*12=@510Z

A$$!(,ar ! %#r! 1* $# a a.,ra! III #$&,#r (#r&a6

A$$!(,ar ! %#r! 0* $# a a.,ra! III #$&,#r #rra'a6 P 1 P 0*@ 10Y6

ETA3A =:

SOLUO NUM$RICA DE SISEMA LINEARES

O Cl()l! N)r,(! &# "!r !b#&,! #$&)'ar #$<)#a$ %)r,(!$ 8al+!r,&!$%)r,(!$;"ara r#$!l)! '# "r!bl#a$ <)# "!'# $#r r#"r#$#%&a'!$ "!r ) !'#l!a&#&,(!6 U #$<)#a #.,(,#%&# <)a%'! #$&# a"r#$#%&a $!l)#$ '#%&r! '# )a

 "r#(,$! '#$#a'a (! ()$&! (!")&a(,!%al 8&#"! '# ##()! #?r,a; ba,!6 O$#$<)#a$ %)r,(!$ %!$ .!r%#(# a"r!,a#$ "ara ! <)# $#r,a a $!l)! #a&a '!

 "r!bl#a6 O$ #rr!$ (!#&,'!$ %#$&a a"r!,a! $! '#(!rr#%&#$ 'a ',$(r#&,9a! '! "r!bl#a* !) $#a* "a$$ar '! !'#l! a&#&,(! "ara ! #$<)#a %)r,(!* # 'a .!ra(!! a$ <),%a$ r#"r#$#%&a !$ 'a'!$ %)r,(!$6

C!%(#,&!$ b$,(!$* <)# ,r! .a(,l,&ar a (!"r##%$! '!$ &!'!$ %)r,(!$

a"r#$#%&a'!$6 A l+#bra l,%#ar # ,$$! $# '## a! .a&! '# <)# !$ r#$)l&a'!$ 'a l+#bral,%#ar* # +#ral* # 'a &#!r,a '!$ #$"a!$ #&!r,a,$* # "ar&,()lar* %a a%l,$# %)r,(a &! +ra%'#* <)# #$&)'! "!r#%!r,9a'! '#$$#$a$$)%&!$ (a'a #9 a,$ $# )$&,`(a6 O

 "r,#,r! ! (!%)%&! '!$ #&!r#$ 'a +#!#&r,a* '#`%,'!$ a&ra$ '# $#+#%&!$!r,#%&a'!$* # ! !)&r! ! (!%)%&!'a$ a&r,9#$ r#a,$ %6A "r,#,ra ,$&a "!'# "ar#(#r <)# &a,$ (!%)%&!$ %! "!$$)# %a'a # (!)6 Ma$ %! b# a$$, (!%.!r#!$&rar#!$ a $#+),r6 N! (!%)%&! '!$ #&!r#$ #$& '#`%,'a )a a',! '!&a'a 'a$

 "r!"r,#'a'#$ (!)&a&,a* a$$!(,a&,a* al 'a #,$&%(,a '! #l##%&! %#)&r! 8#&!r%)l!; # '! !"!$&!6 Al ',$$!* "!'#!$ )l&,"l,(ar ) #&!r "!r ) %#r! r#al6

Err!$

Page 14: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 14/21

 Na b)$(a 'a $!l)! '! !'#l! a&#&,(! "!r #,! '! (l()l! %)r,(!* !$#rr!$ $)r+# '# r,a$ .!%&#$ # #r#(# (),'a'! #$"#(,al6 D! (!%&rr,!* "!'#-$# (#+ar a r#$)l&a'!$ ',$&a%&#$ '! <)# $# #$"#rar,a !) a& #$! !b&#r !)&r!$ r#$)l&a'!$ <)# %!& %#%)a r#la! (! a $!l)! '! "r!bl#a !r,+,%al6

A$ "r,%(,"a,$ .!%&#$ '# #rr!$ $! a$ $#+),%&#$:

Err!$ %!$ 'a'!$ '# #%&ra'a

Err!$ %! #$&ab#l#(,#%&! '! !'#l! a&#&,(!

Err!$ '# arr#'!%'a#%&!$ ')ra%&# a (!")&a!

Err!$ '# &r)%(a#%&!$* #

Err!$ )a%!$ # '# <),%a$6C!%#r$! '# Ba$#: Ar,&&,(a '# 3!%&! Fl)&)a%&#

C! ! !b#&,! '# .!r%#(#r )a ,'#,a '! <)# !(!rr# %! "r!(#$$! '# )'a%a '# ba$# '# ) %#r!* a"r#$#%&a-$# a $#+),r* a (!%#r$! '! $,$&#a '#(,al "ara ! b,%r,! # ,(#-#r$a* "ara '#"!,$ ab!r'ar ! $,$&#a 'a ar,&&,(a '! "!%&! .l)&)a%&# <)#a$ <),%a$ )&,l,9a "ara r#"r#$#%&ar !$ %#r!$6

Err! '# Tr)%(a#%&!

4)r+# (a'a #9 a,$ <)# $# $)b$&,&), ) "r!(#',#%&! a&#&,(! ,%.,%,&! "!r ) "r!(#$$! .,%,&! !) ',$(r#&!

163a$$!

C!%(#,&!$ ,%&r!')&?r,!$ '# $,$&#a$ l,%#ar#$  U&,l,9!)-$# ) ##"l! a"l,(a'! a! $#&!r ,!b,l,r,! %a (,'a'# '# A"ar#(,'a '!

 N!r&#6 A&ra$ 'a a<),$,! '# ) &#rr#%! # '#&#r,%a'! ba,rr! 'a (,'a'# (!

 "a+a#%&! "ar(#la'! "!r ) "#r!'! '# 2 #$#$ !) $#,$ a%!$6 É %#(#$$r,! l#brar <)# ! IG3-M a())la&,!* !) $#a* #l# a(r#$(#%&a'! $#"r# $!br# ! l&,! r#a)$&#6

4#%'! a$$, ) &#rr#%! (!"ra'! %#$&# "la%! &## al&#ra! '# "r#! (,%(! #9#$* !)

$#a* ) r#a)$&# "!r a%! a "ar&,r '! $#+)%'! a%!* <)# ! al!r '! "r,#,r! a%!

.,a'! "#la ,!b,l,r,a6 3ara a"l,(ar a R#+ra '# Cra#r .!, 'a'! %!#$ a #$$#$ 'a'!$

!b&,'!$6 3!r&a%&! ! %#r! '# #$#$ "a+! %! '#(!rr#r '! "la%! .!, r#"r#$#%&a'! "!r *

! al!r 'a$ "ar(#la$ .!, r#"r#$#%&a'! "!r S # ! al!r a"r!,a'! '! IG3-M .!,

r#"r#$#%&a'! "!r 96 O* ! al!r '! IG3-M #$& a"r!,a'! "!r<)# !$(,l!) $#+)%'! a,%.la! '! "a$* $!.r#%'! ar,a#$ '#%&r! '! a%!6 C! #$$a$ &r$ ,%(?+%,&a$ a"l,(!)-$#

Page 15: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 15/21

a .?r)la "ara #%(!%&rar "r,#,ra#%&# ! al!r '! '#&#r,%a%&# # l!+! a"?$ #%(!%&r!)-

$# ! al!r '# (a'a ,%(?+%,&a r#$"#(&,a#%&#6 3ara (!#ar ! '#$#%!l,#%&! '!

4,$&#a '# E<)a#$ L,%#ar#$ & a$ $#+),%&#$ ,%.!ra#$: ! %#r! '# #$#$

r#"r#$#%&a'! "!r * ! al!r "ara S #ra R X*X0 # ! al!r '! IG3-M* r#"r#$#%&a'! "#la

l#&ra 9* <)# #$&aa 9#ra'! %! "r,#,r! a%!* "!,$ ! IG3-M $? .!ra (!bra'! a "ar&,r '!

$#+)%'! a%! # ! al!r &!&al "a+! %! a%!6 A<), #$&a '#!%$&ra%'! !$ &r$ "r,#,r!$

a%!$6 P2 PX*X0 cP0

3a$$! 2C!%$,'#rar ) (,r(),&! #l&r,(! r#"r#$#%&a'! "!r:

{  i2+¿ i2+¿ i3=0 z

1 i

1+¿  z

2i

2  ¿0

 z2 i1+¿  z3i3   ¿120

O%'#*   i1 * i2   # i3 $! a$ (!rr#%&#$ #  z1 P10*  z2 P Y #  z3 P =* a$

,"#'d%(,a$ "#la$ <)a,$*a$ (!rr#%&#$ "a$$a6

A r#$"#,&! '! $,$&#a l,%#ar +#ra'! "#l! (,r(),&! #l&r,(!* "!'#!$ a.,rar:

I > ! '#&#r,%a%&# 'a a&r,9 ,%(!"l#&a A '! $,$&#a 11Y

II >a a&r,9 ,%#r$a '# A* '#%!&a'a "!r A-eP [0,20 0,02 0,07

0,25

1

−0,09 0,08

0,07 0,15 ]III > ! $,$&#a "!$$#l # '#&#r,%a'! 8$,$&#a (!"a&#l; # a $!l)! 'a'a "!rP

i1  P X*X i2 P@*11 i3 P-1=*X

Page 16: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 16/21

O%'#* # $! a$ (!rr#%&#$  z1 P10*  z

2 P Y #  z3 P =* a$ ,"#'d%(,a$ "#la$ <)a,$ a$

(!rr#%&#$ "a$$a6

 z1

P0 P10

-  z1 P P Z5 P Y

-  z1 P 120 P =

 z2 P 0

 z2 - Y6 P Z5

 z2=8.3 .=120

 z3 P 0

 z3 Y6 > =6 P 120

R#$"#,&! '! $,$&#a l,%#ar +#ra'! "#l! (,r(),&! #l&r,(!* "!'#!$ a.,rar:

I –  ! '#&#r,%a%&# 'a a&r,9 ,%(!"l#&a A '! $,$&#a 11Y6

D#&A:

Y6Y-=68-Y-10; P D#&A P Y6Y =81Y;

D#&A P Z@ 5@ P D#&A P 11Y

Page 17: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 17/21

II – a a&r,9 ,%#r$a '# A* '#%!&a'a "!r A-eP [0,20 0,02 0,07

0,25

1

−0,09 0,08

0,07 0,15 ]

AP 1 1 1 C!.A P -2@ =0 -Z@ 8C!.A;& P -2@ =0 -Z@

10Y 0 =0 -YY 0 =0 -YY 0

Y0 -= -Z@ 0 Z -Z@ 0 Z

III – ! $,$&#a "!$$#l # '#&#r,%a'! 8$,$&#a (!"a&#l; # a $!l)! 'a'a "!rP

i1  P X*X i

2 P@*11 i3 P-1=*X

D#&A ,1 P P -168-=6Z5; 8-Y6120; P -Z5 P D#&A ,1

D#&A ,2 P P 168120610 > Y6Z5; 61 8-=6Z5; P @Y5 P D#&A ,2

1 1 0

D#&A ,=P 10 Y Z5 P 16Y6120 > 16 8106120 > Z56Y; P 2Y0 P D#&A ,=

Y 0 120

i1 P D#&A ,1 P - Z5 P - Z*@Y

D#& A 11Y

i2  P D#&A ,2 P @Y5 P @*11

D#& A 11Y

i3  P D#&A ,= P 2Y0 P 2*=

D#& A 11Y

I – ! '#&#r,%a%&# 'a a&r,9 ,%(!"l#&a A '! $,$&#a 11Y6

E$&a a.,ra! (!rr#&a* "!,$ ! '#&#r,%a%&# (!rr#$"!%'#* D#&A P 11Y

Page 18: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 18/21

II –  a a&r,9 ,%#r$a '# A* '#%!&a'a "!r P -eP [0,20 0,02 0,07

0,25

1

−0,09 0,08

0,07 0,15 ]

E$&a a.,ra! #$& ,%(!rr#&a ,$&! <)# a a&r,9 ,%#r$a ',.#r#%&# 'a a&r,9

a"r#$#%&a'a

III – ! $,$&#a "!$$#l # '#&#r,%a'! 8$,$&#a (!"a&#l; # a $!l)! 'a'a "!r:

P   i1  P X*X i

2 P@*11 i3 P-1=*X

E$&a a.,ra! #$& (!rr#&a "!,$ a $!l)! #%(!%&ra'a ,+)al a 'a $!l)! a"r#$#%&a'aP

X*X P @*11 P -1=*X P P X*X P @*11 P -1=*X

3a$$! =C!%(l)$! '! N#r! 3ar(,al '! C?',+! '# Barra$ 3al%'r!!

A$$!(,ar ! %#r! 0* $# a a.,ra! I #$&,#r (#r&a6

A$$!(,ar ! %#r! 1* $# a a.,ra! I #$&,#r #rra'a6

A$$!(,ar ! %#r! 0* $# a a.,ra! II #$&,#r (#r&a6

A$$!(,ar ! %#r! 1* $# a a.,ra! II #$&,#r #rra'a6

A$$!(,ar ! %#r! 1* $# aa.,ra! III #$&,#r (#r&a6

A$$!(,ar ! %#r! 0* $# a a.,ra! III #$&,#r #rra'a6

#*))- 4

RELAORIO 3:S-() </>,*) =( ),).(/* =( (@*() ,<(*()*.(1M&!'!$ ',r#&!$ (al()la a $!l)! '# ) "r!bl#a # ) %#r! .,%,&! '# "a$$!$6

E$&#$ &!'!$ r#$)l&ar,a %a r#$"!$&a "r#(,$a $# #l#$ .!$$# r#al,9a'!$ (! "r#(,$!

,%.,%,&a6E#"l!$ ,%(l)# a El,,%a! Ga)$$,a%a* ! &!'! '# .a&!ra! '# $,$&#a$

l,%#ar#$ '# #<)a#$ # ! al+!r,&! $,%"l# '# "r!+raa! l,%#ar6 Na "r&,(a* )&,l,9a'a

 "r#(,$! .,%,&a # r#$)l&a'! )a a"r!,a! 'a $!l)! r#al 8a$$),%'! #$&ab,l,'a'#;6

E (!%&ra$&# a!$ &!'!$ ',r#&!$* &!'!$ ,%&#ra&,!$ %! &#r,%a # )

Page 19: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 19/21

'#&#r,%a'! %#r!$ '# "a$$!$6 A&r,b)'! ) al!r ,%,(,al *&!'!$ ,%&#ra&,!$

r#al,9a $)(#$$,a$ a"r!,a#$ <)# (!%#r+# "ara $!l)! #a&a # $#) <)a%'!

)a $!l)! $).,(,#%&##%&# "r#(,$a .!, #%(!%&ra'a6

M#$! )$a%'! )a "r#(,$a ,%.,%,&a* #$&#$ &!'!$ 8+#ral#%&#; %! (#+ar,a $!l)! # ) %#r! .,%,&! '# "a$$!$6 E#"l!$ ,%(l)# ! &!'! '# N#W&!% *

&!'! '# b,$$#(! # a ,%&#ra! '# Ja(!b6 E a&r,9#$ '# l+#bra (!")&a(,!%a,$*

&!'!$ ,%&#ra&,!$ $! +#ral#%&# %#(#$$r,!$ "ara "r!bl#a$ (!"l#!$6

M&!'!$ ,%&#ra&,!$ $! a,$ )$)a,$ '! <)# &!'!$ ',r#&!$ # a%al,$# %)r,(a6

Al+)%$ &!'!$ $! ',r#&!$ # $#) "r,%(,",!* a$ $! )&,l,9a'! (!! $# %! .!$$#

#6+ &!'! '# r#$')! %,! +#%#ral,9a'! # ! &!'! '! +ra',#%&# (!%)+a'! 6 3ara

#$&#$ &!'!$ ! %)#r! '# "a$$!$ %#(#$$r,!$ "ara $# !b&#r a $!l)! #a&a &! +ra%'#

<)# a a"r!,a! a a(#,&a 'a #$a a%#,ra <)# %! &!'! ,%&#ra&,!6

CONCLUSO

  C!%.!r# !$ '#$#%!l,#%&!$ .!ra !l&a'!$ a!$ "a$$!$ 'a$ #&a"a$ # !$ (l()l!$

'#$#%!l,'a$ a$ $,&)a#$ "r!"!$&a %!$ '#$a.,!$ .!ra '# #&r#a ,"!r&d%(,a "ara

#%(!%&ra!$ !$ (?',+!$ '# barra$ <)# !b#&,! "r,%(,"al '! %!$$! &rabal! a$$,

,#!$ a #%(!%&rar a R#$!l)!: O (?',+! '# barra$ l,%#ar "al%'r!! (!"l#&! (! !$

l&,!$ 1 al+ar,$!$: 8 1110110001110010110100111000110111 ;6

3!r ., .!, #lab!ra'! %#$&a A&"$* ) r#la&?r,! $!br# 4!l)#$ %)r,(a$ '#

$,$&#a '# #<)a#$ l,%#ar#$ "ar&# 1 # "ar&# 2 * (!! &ab al+)a$ r#$!l)#$ '#

(l()l!$* !%'# .!ra )$a'a$ ',#r$a$ .#rra#%&a$* "ara (al()lar # )$&,.,(ar &!'a$ #&a"a$*

'a%'! (!%(l)$! .,%al '# &!'!$ !$ '#$a.,!$ '! (?',+! '# barra$ #%&r# a$ #$a$ #

(!%(l),%'!6

Page 20: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 20/21

REFERENCIA BIBIO"RAFICA

HATTORI* M6 T6 H6 f UEIROc* B6 C6 N6 M&!'!$ # 4!.&War# N)r,(!$6

D#"ar&a#%&! '# 4,$&#a$ # C!")&a!* U%,#r$,'a'# F#'#ral '# (a",%a Gra%'#*

Ca",%a Gra%'#* 1XX5

RUGGIERO* M6 A6 G6 f LO3E4* V6 L6 R6 Cl()l! %)r,(!: a$"#(&!$ &#?r,(!$ #(!")&a(,!%a,$6 26#'6 4! 3a)l!* Magr!%* 1XX

Fra%(!* N#,'# M6 B6 Cl()l! N)r,(!6 1 #'6 4! 3a)l!6

R)++,#r!* Mar(,a G6 Cl()l! N)r,(!* A$"#(&!$ T#?r,(!$ # C!")&a(,!%a,$6 2 #'6

4! 3a)l!6

Page 21: elizaldo

7/23/2019 elizaldo

http://slidepdf.com/reader/full/elizaldo 21/21