Upload
pham-thi-thanh-thuy
View
8
Download
1
Embed Size (px)
Citation preview
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 1/10
Math2IT
Dinh Anh Thi | 31.10.14 | Hiu ton hc | Ton cao cp | 7Like
Tnh hp l ca nghim h phung trnh v khinim 'condition number' ca mt ma trn (k 1)
Bn s tm hiu th no l mt h phung trnh iu kin yu v iu kin mnh, chun ca mtma trn, condition number ca ma trn l g v nh hng ca n ti nghim h phung trnh rasao?
Bi vit tham kho t trang Mathematics for College v bi ging ca Dheeraj Bhardwaj. Bncng c th ti bn pdf nguyn gc (bng ting Anh) ca trang ny ti a ch
Math2IT | Download course
k 1 ny, bn s bit c
S khc nhau gia h phung trnh iu kin yu (ill-conditioned systems of equations) vh phung trnh iu kin tt (well-conditioned ).nh ngha v tm chun ca mt matrix (norm of a matrix).
k tip theo, bn s bit c:
nh ngha v cch nh gi condition number ca mt ma trn kh nghch.
Lu : nguyn tc ca blog l khng dch thut ng ting nc ngoi nhm m bo chnh xc v gip bn c th t tm kim thm ti liu tham kho nu mun.
TRANG CH LATEX TON LINUX OS X CNTT TRI THC KHC MATH2IT tm
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 2/10
Mi quan h gia condition number ca mt ma trn vi cc iu kin mnh yu ca mth phung trnh tuyn tnh v bn c th tin bao nhiu phn vo nghim ca cc h ny?
Chng ta cng bt u bi vit bng vic xt dng tng qut ca h phung trnh nh sau:
H phung trnh iu kin yu v mnh l g?Mt h phung trnh c gi l ill-conditioned nu s thay i nh cc h s ca ma trn hoc s thay i nh trong v phi dn n s thay i ln trong vector nghim .
Mt h phung trnh c gi l well-conditioned nu s thay i nh cc h s ca ma trn hoc s thay i nh trong v phi dn n s thay i nh trong vector nghim .
V d 1 - ill-conditioned system of equationsXt h phung trnh sau y
H phung trnh ny c nghim l
Thay i mt cht v phi ca h
s cho ta nghim mi l
Cn nu ta thay i mt cht cc s trong ma trn
ta s nhn c nghim
4
5
4
5
4
5
4
5
4
5
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 3/10
C hai nghim mi nhn c ny iu khc xa nghim c d ta ch thay mt cht t gi tr cch s. Do , ta ni h phung trnh trong trng hp ny ill-conditioned.
V d 2 - well-conditioned system of equationsXt h phung trnh
H ny c nghim
Cng tung t trn, ta tin hnh thay i mt cht t v phi ca h
khi nghim mi l
Cn nu ta thay i trong ma trn v tri
v nghim mi l
C hai nghim mi nhn c ny iu thay i rt t so vi nghim c khi c s thay i t v phi hay ma trn h s. Ta ni h ny well-conditioned.
Nu h phung trnh l ill-conditioned, ta khng nn tin tng qu nhiu vo nghim. S d nh
4
5
4
5
4
5
4
5
4
5
4
5
4
5
iu g s xy ra nu h phung trnh l ill-conditioned hay well-conditioned?
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 4/10
vy v bn th ngh xem, mi khi bn gii mt phung trnh no , hoc bn chuyn t bi tonthc t sang vic phi gii mt h phung trnh tuyn tnh, bn mun th vi nhiu h s khcnhau thy s thay i ca nghim. Trong khi bn ch thay i rt rt t h s, vy m nghimli sai khc mt s rt ln. Bn c hi lng c iu ny khng?
k tip theo, chng ta s i tm hiu chng ta c th tin bao nhiu phn vo nghim ca mtphung trnh, cch tin l nh th no. Mi ma trn kh nghch u c mt condition number vmt machine epsilon, da vo hai lng ny, chng ta c th nh lng xem bao nhiu con strong kt qu nghim l ng tin cy.
c th tnh c condition number ca mt ma trn nghch o, ta cn phi bit trc chunca ma mn l g v lm cch no c th xc nh c n.
Chun ca ma trnCng ging nh nh thc (determinant) ca ma trn, chun ca ma trn cng l mt i lngv hng (scalar number). Tuy nhin, chun th lun dung phi c nh ngha cho tt ccc ma trn (bt k ma trn vung hay ma trn ch nht, ma trn kh nghch hay khng).
Chun ca ma trn c nh ngha tung ng vi chun ca vector c cho bi
Chun ca ma trn o c sc nh hng ca s thay i trong ma trn n s thay i trongvector nghim.
Mt trong nhng nh ngha ph bin ca chun ma trn l tng tr tuyt ln nht theo ct(maximum absolute column sum). Chun ny c tnh bng cch ly tng tt c cc h s trnmi ct ri so snh gia cc gi tr vi nhau, gi tr no ln nht chnh l chun ca ma trn. ivi ma trn dng ct,
nh ngha th hai l tng tr tuyt ln nht theo dng (maximum absolute row sum),
V d 3Vi ma trn
NBY
4
4
4
) *
] ]
NBY
&)
%
*
%&
] ]
NBY
%*
&
)
%&
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 5/10
Khi y,
Mi bn n xem k tip theo.
7peoplelikethis.Bethefirstofyourfriends.Like
Dinh Anh Thi : Tc gi blog, xut thn l sinh vin s phm ton, hin ang l nghincu sinh v Ton ng dng ti Php. Chnh v nim am m Ton hc, tin hc ng dngv qua trng lp s phm nn Thi rt quan tm n vic ng dng Ton hc, Tin hcvo trong cuc sng thc t cng nh vic truyn t kin thc Ton cho hc sinh theomt phung php hin i v tch cc nht, gy hng th v hiu su cho ngi hc,ngi c ni chung. Mi chi tit xin lin h [email protected]. Blog c nhnAnh Thi blog.
] ]NBY
%
&
%&
NBY ]] ] ] ]] ] ] ]] ]] ]] ] ] ]]
NBY
31.10.14 , Hiu ton hc Ton cao cp
Vit bi cng blog bng cch lin h [email protected].
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 6/10
Tnh hp l ca nghim hphung trnh v khi nim
'condition number' ca mt ma trn (k1)
Bi lin quan
Bi ng C hn
Tont'Lnutrang'(Backtotop)cunmtchoBlogger1comment6monthsago
VietOverlandTravelCmnbnnh.Itworksperfectly:)!!!Vietnamoverlandtours
Tophntrangcnhschoblogger16comments5monthsago
Tiliuminphcamnadmnhlmthnhcngri@@@!!
CchtofilevnbnbngLaTeX21comments5monthsago
haduyanhCmnbnnh.Mnhsacri
Quyctrongtonhc?8comments5monthsago
nonameTrongtonhcngitakhngaiiquyciucthchngminhc.Vycuhitisaonhtrnthy"chngminh"
ALSOONMATH2IT
0Comments Math2IT Login
SortbyBest Share
Startthediscussion
Bethefirsttocomment.
WHAT'STHIS?
Subscribe AddDisqustoyoursited Privacy
Favorite
Bi ng Mi hn
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 7/10
Chuyn file hnh trong Matlabsang code hnh v trong LaTeX
Tuyn tp ti liu v phngphp phn t hu hn (Finite
Element Method) - cp nht websites
Tuyn tp ti liu gii tch hm(Functional Analysis)
Tuyn tp cc eBooks hiu thmv th gii ton hc k th (cp
nht ngy 10/12/2014)
Gii thiu
Math2IT l chuyn trang v Ton hc+ Gio dc v Cng ngh. Mongmun chia s tri thc v kht khao imi nn gio dc nc nh. cthm.
Theo di chng ti
+38 xut url ny trn Google
Nhiu nht 7 ngy qua
Nhng cch v hnh chnh xcbng thc k v compa
Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin
bn khc
Nhng phn mm nn ci choUbuntu, Elementary OS, Linux
Son tho ton hc trong LaTeX(k 1)
Math2ITTon&Tin1,461Like
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 8/10
WolframAlpha : gii ton theotng bc
Tng hp nhng vic cn lmsau khi ci Windows c mt
chic my tnh y mnh m
Ti liu tham kho dnh cho itng t hc LaTeX (cp nht
ngy 6/11/14)
Bi ngu nhin
Chuyn ton: a v bi ton bit
Chuyn ton: Con ng mica cc nh ton hc
TeXTips: Hin th php ton tonhc ging nh hi tiu hc
TeXTips: Chn nhiu hnh phtrong mt hnh chung
TeXTips: Lm cho cng thc tonthng ng trong LaTeX
Nhiu nht 30 ngy qua
Nhng cch v hnh chnh xcbng thc k v compa
Nhng vic cn lm sau khi ciUbuntu 14.04 v mt s phin
bn khc
Nhng phn mm nn ci choUbuntu, Elementary OS, Linux
Ti liu tham kho dnh cho itng t hc LaTeX (cp nht
ngy 6/11/14)
Son tho ton hc trong LaTeX(k 1)
WolframAlpha : gii ton theo tng bc
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 9/10
Google+
Math2IT
+ 38
Theo di
Lt xem
111191
Nhn xt mi
Ti liu min ph
bn c th cho mnh xin link face cabn.. mnh c th trao i trc tip vibn.. bn gip...
To phn trang c nh s cho blogger 2 hours ago
inh Anh Thi
a, mnh thy n khi n lch th mi pm bn, khi y th cc bi n "kht" lic vi nhau...
To phn trang c nh s cho blogger 3 hours ago
Ti liu min ph
Bn inh Anh Thi cho mnh hi thm ciny na nh !! hjhj trn trang ch blogbi ng n c b...
To phn trang c nh s cho blogger 12 hours
ago
inh Anh Thi
Hix, mnh cng nh mua n bn, mnhkhng r bn i, thng th bn nn hicng ty bn tn min...
1/15/2015 Tnhhplcanghimhphungtrnhvkhinim'conditionnumber'camtmatrn(k1)|Math2IT
http://math2it.blogspot.fr/2014/10/tinhhoplycuanghiemhephuongtrinh.html 10/10
ANDROID BLOGGER-BLOGSPOT CHUYN TON HC
EBOOK GAME GIO DC HIU TON HC
HI P HI P LATEX HI P TIN
HI P TON KHC KHM PH
KIN THC CNG NGH KIN THC THPT LATEX
LINKS LINUX LI LATEX MATH2IT OSX
PHN MM TEX CHUYN NGNH TEXTIPS
TH THUT IT TON TON CAO CP TON S CP
TI SAO T HC LATEX THI VUI
To phn trang c nh s cho blogger 1 day ago
Theo di qua email
Emailcabn... SUBMIT
Chuyn mc
2012 Math2IT | Thit k bi Template Trackers | Chnh sa bi inh Anh Thi