I HC BCH KHOA TPHCM

PHNG PHP TNHI Sai s : Cng thc sai s tng i:

Sai s quy trn: vi s gn ng a c quy trn thnh a*

Sai s tuyt i ca a* so vi s ng A :

Lm trn lnBi ton c trng :

Bit A c gi tr gn ng l a vi sai s tng i l . S a c quy trn thnh s a*. Hi sai s tuyt i ca a* l bao nhiu?

Gii : : lm trn ln Sai s hm s : trng hp hm 2 bin

Lm trn ln

V d: Cho hm s

Bit . Tnh

Vi ta c . Lm trn ln Ch s ng tin: Ch s th k sau du phy ca s gn ng gi l ch s ng tin

Cng thc ph: (Vi l tr tuyt i phn nguyn ca s A)

V d: Nu vi

Ta c: . tng ch s ng tin ca a l 4 ch s. (Gm 3 ch s ng tin sau du phy).II Gii phng trnh gn ng:

Gii phng trnh

Khong cch li nghim: Phng trnh c khong cch li nghim l nu v n iu trn . Gi s phng trnh trn c nghim gn ng th ta c sai s:

Vi v Sai s lm trn ln

V d: Cho phng trnh c khong cch li nghim l c nghim gn ng l nh gi sai s ?

Ta c:

Xt

Vy hm s n iu trn

M

Suy ra:

Cch bm my o hm ti 1 im. Nhn

Mn hnh hin th: bm = l xong.Cc phng php gii gn ng phng trnh:1/ Phng php chia i:

Gi s phng trnh c nghim trong khong cch li nghim l . Tm nghim gn ng ca phng trnh trn.Phng php:V trc ta vi hai u mt l gi tr khong cch li nghim.

Chia i ly gi tr trung bnh l

Xt du ca (t du + hoc vo gi tr ca ) c hai u tri du th ly khong chia i tip tc nh th cho n khi yu cu bi tha mnSai s ca phng php chia i l:

Lm trn ln

V d: Tm nghim gn ng ca phng trnh theo phng php chia i: trong khong cch li nghim

Sai s: lm trn ln2/ Phng php lp n:

Trc tin tm theo cng thc: nu th p dng c phng php ny.( lm trn ln)

Phng php: a phng trnh v dng . Chn ty . Thc hin vng lp theo cng thc

Bm my: Cng thc sai s tin nghim :

Lm trn lnCng thc sai s hu nghim :

Lm trn lnNghim lm trn qu bn

Ch : Nu bit trc ta c th tnh trc s bc cn lp theo cng thc sai s tin nghim vi sai s cho trc theo cng thc:

Vi l phn nguyn ca s A

3/ Phng php lp Newton: (Ch : Hm s phi l hm n iu trn a,b. Nu tn ti 1 im c thuc khong cch li nghim th ta dng phng php chia i kh c ri mi dng Newton)Phng trnh lp l

Phng php lp ny ging nh trn Cng thc nh gi sai s:

Lm trn ln im Fourier: Mt im c gi l im Fourier ca hm nu

Quy c chn im l im Fourier trong phng php lp Newton l mt trong 2 u mt a hoc b.

Nu

V d: Cho phng trnh trong on . nh gi sai s nghim gn ng

Xt

im Fourier l 2. Chn

Vy

Dng phng php lp Newton ta c:

Sai s: III Gii gn ng h tuyn tnh:

1/ Phn tch ma trn tng qut (Phng php Doolittle)

Vi A l ma trn cp 3:

Ma trn L c dng sau :

Ma trn U c dng:

Dng my tnh nhp ma trn A v ma trn L. Gn ma trn A l MatA, L l MatB. Bm

Vi A l ma trn cp 2:

Ma trn L c dng sau: Tng qut A l ma trn cp n:

Th ma trn L c dng tng qut sau: V U tnh tng t nh trn.2/ Phng php phn tch Cholesky:

Phn tch tng t nh phng php Doolittle. Nhng A phi l ma trn i xng v xc nh dng. Vi

A l ma trn cp 3:

Th B c dng: Hoc c th theo cng thc gn hn:

vi cc phn t

i vi A l ma trn cp 2:

Th ma trn B s c dng

Cch tm tng cc phn t nhanh:

Gi s ma trn A c dng a A v ma trn bc thang nh sau:

Khi 3/ Chun vector:

Cho vector

Chun hng ca vector x l:

Chun ct ca vectorx l: Tnh cht: Chun vector lun lun dngChun vector bng 0 khi l vector 04/ Chun ma trn:

Cho l ma trn cp n th chun:

Hng: hay pht biu nh sau: Tng cc hng, hng no c tng ln hn th l chun hng

Ct: hay pht biu nh sau: Tng cc ct, ct no c tng ln hn th l chun ct

Tnh cht: , , S iu kin ca ma trn:

vi ty bi yu cuCch bm my chun hng ct: Nhp ma trn MatA l ma trn bi Tnh chun hng th nhp MatB nx1. Dng lnh: Abs(MatA).MatB th s tm c Tnh chun ct th nhp MatB 1xn. Dng lnh: MatB . Abs(MatA) th s tm c Vi Abs() bng cch SHIFT + huyp5/ Phng php lp Jacobi gii h phng trnh:Phng php:

a h v dng:

Kim tra iu kin (Hng hoc ct)

Ly l vector gi tr ban u bt kDy lp theo cng thc:

nh gi sai s:Tin nghim:

vi q ty theo sai s theo chun hang hay chun ct.Lm trn lnHu nghim:

vi q ty theo sai s theo chun hang hay chun ct.Lm trn lnQuy c ly cng mt loi chunV d: Gii gn ng h sau:

Dng phng php lp Jacobi ta c:

. D thy v

Chn

Tng t:

Sai s: Bm my:

Chng no xut hin D, X, Y th l gi tr ca vector

6/ Khi nim ma trn cho tri: A c gi l ma trn cho tri khi tng ca bt k mt hng tr phn t ca hng b hn .

7/ Phng php Gauss Seidel: Cc thnh phn ca va tnh c dung tnh trong bc tip theo

Ma trn lp Gauss Seidel :

Th ma trn lp s l vi

v Bm my:

Chng no xut hin D, X, Y th l gi tr ca vector Cch bm my khc:

Vi v d: Tnh vector vi vector ban u

Bm my:

Tng t A, B xut hin k ln l .[12]