Báo cáo môn phương pháp tính Hệ phương trình đại số tuyến tính

 Ths. Nguyễn Văn Phú  BK10HTĐ            !   "#!$%   &'(%)   %)*   %)* +,   -   %)*.!(   &'(.(-   %)*/0%)$ 1234565789:                          ;<;   !  "#$%& '()* +, -,  "#5=>?@@=A A. !&.&-/&01& B. 2&#3 C. 2-2 "#55&"#B%)$AC A. !&.&-/&01& B. 2&#3 C. 2-2 "#555D"#A+?'@=%)$EAFG A. !&.&-/&01& B. 2&#3 C. 2-2 "#5H@%)IJIK(ALM A. !&.&-/&01& B. 2&#3 C. 2-2 "# '!(E-ANF A. !&.&-/&01& B. 2&#3 C. 2-2 "#5&"#A+-AGO A. !&.&-/&01& B. 2&#3 C. 2-2  8P5 QR ST5Q UVWXYZ FUF5Q 45-6 7&89:2&8 ;$ <= >-2? @? a <= >-2?9 '? ;$ ABC;6-2aDAE> -2$F3 $GAHB1C ACICJ:2<= KL&0&1 MA&M&;&M 4N-<=OPQAP<= >-2?&#&R '?9M&R &1BKM CIS1&AB&<T -<=5&N-<=K<U  2S% 2&?&&MVW C6 PAQP  EH <= >-2?&06&? '?9X I&Y EH& !Z Q  A[  EH 0\&M&R &1&]<T :1& I&Y EHK<TKNAO   @?&<U? '?9M:TA-2N-<=  <= &;&^M I &Y Z  O MW&<=3B1CIS1&AB& !&J&0&1  O FUM[5\X5]Q1&&^ SF&C_5&?&#33`2M a !&J:1&K<TKN EH -2&b5&?&F33`&^M  :1&EH-2Sc5&?   7?S\ 3dKF F&#33`J<= 5&?.>U:29F& M:T &F0Z:2 >?-2&b-2Me &^MWC6Z f!&J3&SJ.><Z4J-2&b1 7?&YCKF F &#33`B&$%& 7?&YC[-2"1B&&g-\5&U:8h b1B7 0\ 7?@!Sc3I&X 7?&@?&R R 'M:T <= >-2?-2&b OPP  !?&06&? 'M:TA<= < PP[PQAP  O V )_ V M!!C-2&b?&g-\fM\&M&R &1&;&M &&-2&b  3%3&M&B G\-2&bC1&]d ? L <=3-2&b?&MSF&i&Y B&jK,  C6-2&b -\:2-2&b$?2&b-\0-2&b$? -</1 WSF& i&Y  fM:T?&06&?  M  :1&&`33`EH '?B 7?<= > -2&B1   C M&<=3<= -NB 7?<= >-2CI& FUL[5]X5]Q1&&^_6Y` \`0 9&V&_S20  :1&?&#33`0\B:6 &R 6 &\0&;3Y &N3U^M]0<T B?&R KF F5<= &J6 &M0&;K<TKN83`:2kS3Z3KFB3a:23 8&8 [U[T51& MU2&b1?-lKF F&#33` '  ?&M  SJ&Y Z HO SHO U[T5T MUH≈ SH≈  8P55 &8P&&&5XYZ UVWXYZ MUF ab!B +, ;  ' <U20-2&_69 '3<U&_Z :T-22-\&, &\CMd!02M! "6 '3<U&_-2&8M MMM&_20& G$%&7 6U I-#3)We&_> B6 '3<U&_-2M25MJ '< M:T&, M2Md!EIC& a$%&CMdH2 &\!&k&NK0F&6 '3<U&_<= >-2CMd  -06 )_& G$%&6U '3<U&_B\12-\&, &\CMd  -0 6&_I&<BJ&_6 '3<U&_ 9&&12  S<T Z <T Z_&F& d  CMd  -06 '3<U&_ <T ZM&XCMd  -06B&_69 '3<U&_ Sm5&3<U332M!:T? M&<T  48-/ !" #$%&'()'*%(&(+  ) no_>  '8-/-2Z5&< M-\&, !J3; ' &, M2p .&&, M2;&F&&NJ"1< M-2U6&_J .&-2K0F& 48-/(dj2-\&, &\MNCd:&M"1-269 '6 ;$ &M:2B1&_& ! I&Y ?&q]& <Z MUM&"#B?c r%&3<U&_ !6 ;$ &MCMd  -06:24e&:2-2 J ;7MN;&8"1&_ ;-26:2KX-N"<= -N &$%&KF '"1Be&"1Be&"<:#0&&<= :25K213&, ] &_ I M1-&<= C1&]d<Z , "<:#0&<= -2KV0&g:2S8 e&\B b-2KV0d:2S8 eK<TM! 9 L5&,X!& !Z I&<&jK, I&Y ?<Z MUL&"#B<a?# 4`0-23<U333qS1Jd3<U&_&MCMd  -06 <T &\& 0J3<U&_:WKN&<U<U&M !6 '3<U&_ b>-2JSF&5 '2f>5&&8 S-2&s/r`0KRKV0-e3&^M I&Y -e3 2&MCdM&R5&, 'KV0BKV0 !5&,:W6 '3<U&_0 CIhR5&,:2TN3,&5 &:2M&8-e3Sh:2 ? L-2 I&Y ? 48o-$./012*/(12* 13 48-/*&'') 48-/)*451*&6 (12) 48-/E"0\-/$N MH(dj-22 M&\MN:T6? M-24k &B!:T>&8SK&MBKV0-e3$ 8&^M I&Y p5&, :W6K0F& '3<U&_:2& ! I&Y ?Z Me Z MUN&"#Bde! (dj  !NM21 F3-\&, :2  NM2 :2 CIqKF&M CMd  -06 Y6 ;$ "1-22C CI:T>&_ 3<U&_&Mp&<U<U:T3<U&_Z 7 f9&p&_M M !Z :2&XWC6:T&&<= *2UdF&&MdVWC620-2:2 9&1 I&Y -e3Z 48-/8519' #4:;  )<'/5=4(>?&@+A#B?: C1DE=(#$%&) f9/Z Q4J? ' I&Y "^t&M&jK, I&Y ?&q]& Q4WC6uM^ G-2WC6'BCI3d-2WC6 XWC6 uM^B& !&J<]0&.  >&8S<Z"1<NM2 F3 :2NM2 F3 LKF&_ >B<= -N > QM33"^t&MBWC6&MCMd  -06-2&\]01&"1 !5& JJ M&_3<U33&<KL-2 IJ-MNScJ!&<T C jK,33"^t&M MUGfD"#A+%)$ M320&_<&jK,/&< '3<U33"^t&Md63<U &_k3<U&_3&01:2v<=3?3<U&__U:2 ?vWU& a$%&&<U&Rr%&6Z :T-2  2-\&, :2 !NM2\&^M  S1:2-\&, &M-` # '6(djZ :T>&M-` # '6!1 >'6&_KV0:2& <= &X I&Y Z p5&,:W66 '3<U&_ [U[T51& FLUw<U&_)K^x-?:T F&C; !KNZ F :TyO&zEM-HBBS-2  m?3,&5 :2M F&C; , &Jh#-23F&h-26&5hG-2&J&; h-2?M-^BHGI-2&J&; M-^ *V0$ 8&J&; M-^: ' F&C;-2 SMKM$K^Ef{  H:2M$0^ E{  HK<T3F&B:2&:26&5B:21&m? :T SMKM$K^& !OBSOh b?:TM$0^& !O BSO J U[T5T FLU !Z ( ) ( ) ( ) ( ) 2 2 2 2 2 3 2 2 3 2 0 ( ) 0 (1) a pv a p v b RT v b RT v v pv a v b v RT pv pbv av ab v RT pv pb RT v av ab   +   + − = ⇔ − =  ÷  ÷     ⇔ + − = ⇔ − + − − = ⇔ − + + − =  4?:TfSMKM$K^Ef{  HZOBSO [3O&BO M  EH⇒ ⇒O [3O&BO M  EH⇒ ⇒O [3O&BO M  EH⇒ ⇒O [3O&BO M  EH⇒ ⇒O [3O&BO M  EH⇒ ⇒O [3O&BO M  EH⇒ ⇒O [3O&BO M  K [...]... 0,144176 0,3 0,3 0 0,409542 0,4 0,409935 Trang 18 Sai số : x ( 7) x Tj x ( 7) x (6 ) 1 Tj 0,111475 0,111442 0,625 = 0,144176 0,144559 1 0,625 0,409935 0,409542 0,000033 0,625 0,625 = 0,000383 = 0,000393 = 0,655.10 3 < 10 3 1 0,625 1 0,625 0,000393 Vậy nghiệm gần đúng của hệ ph ơng trình là: x1 0,111475 x = x (7) = 0,144176 2 x3 0,409935... 413125 Sai số : x (3) x Tj x (3) x (2 ) 1 Tj 0,1203125 0,15 0,625 = 0,1375 0,19375 1 0,625 0, 413125 0,325 x (4) 0,625 = 1 0,625 0,0296875 0,625 0,05625 = 0,088125 = 0,147 1 0,625 0,088125 = Tj x + C j (3) 0,25 0,25 0,120313 0,25 0,112344 0 0,375 = 0 0,25 0,1375 + 0 = 0,148398 0,3 0,3 0,413125 0,4 0,405156 0 Sai số : x ( 4) x Tj... 17 Sai số : x (5) x Tj x ( 5) x ( 4 ) 1 Tj 0,111612 0,112344 0,625 = 0,143418 0,148398 1 0,625 0,410816 0,405156 0,000732 0,625 0,625 = 0,00498 = 0,00566 = 0,00943 > 10 3 1 0,625 1 0,625 0,00566 x (6 ) = Tj x + C j ( 5) 0,25 0,25 0,111612 0,25 0,111442 0 = 0,375 0 0,25 0,143418 + 0 = 0,144559 0,3 0,3 0 0,410816 0,4 0,409542 Sai số : x... 0,375 0 0,25 0 + 0 = 0 0,3 0,3 0 0 0,4 0,4 Sai số : x x (1) Tj x x (1) 1 Tj (0) 0,625 = 1 0,625 0,25 0,625 0 = 0,4 = 0,667 > 10 3 1 0,625 0,4 x (2 ) = Tj x (1) + C j 0,25 0,25 0,25 0,25 0,15 0 = 0,375 0 0,25 0 + 0 = 0,19375 0,3 0,3 0 0,4 0, 4 0,325 Trang 16 Sai số : x (2) x Tj x (2 ) x (1) 1 Tj 0,15 0,25 0,625 = 0,19375 ... 0,9 = 0,1 0 0,2 0 + 0,7 = 0,7 0 0,2 0 0 0,6 0,6 Trang 19 Sai số : x (1) x Tj x (1) x (0) 1 Tj 0,9 0,3 0,3 = 0,7 = 0,9 = 0,3857 > 10 3 1 0,3 1 0,3 0,6 x (2 ) = Tj x (1) + C j 0 0,1 0 0,9 0,9 0,97 = 0,1 0 0,2 0,7 + 0,7 = 0,91 0 0,2 0 0,6 0,6 0,74 Sai số : x (2 ) x Tj 1 Tj 0,07 0,3 = 0,21 1 0,3 0,14 x (2 ) x (1) = 0,97 ... 0 0,2 0 0,74 0,6 0,782 Sai số : x x (3) Tj x x (3) 1 Tj 0,021 0,3 = 0,035 1 0,3 0,042 = (2 ) 0,991 0,97 0,3 = 0,945 0,91 1 0,3 0,782 0,74 0,3 0,042 = 0,018 > 10 3 1 0,3 Trang 20 x ( 4) = Tj x (3) + C j 0 0,1 0 0,991 0,9 0,9945 = 0,1 0 0,2 0,945 + 0,7 = 0,9555 0 0,2 0 0,782 0,6 0,789 Sai số : x ( 4) x Tj 1 Tj 0,0035 0,3 =... 0,6 0,7911 Sai số : x ( 5) x Tj x (5) x ( 4) 1 Tj 0,00105 0,3 = 0,00175 1 0,3 0,0021 x (6) = 0,99555 0,9945 0,3 = 0,95725 0,9555 1 0,3 0,7911 0,789 0,3 0,0021 = 0,9.10 3 < 103 1 0,3 = Tj x + C j (5) 0 0,1 0 0,99555 0,9 0,995725 = 0,1 0 0,2 0,95725 + 0,7 = 0,957775 0 0, 2 0 0,7911 0,6 0,79145 Trang 21 Sai số : x (6) x Tj x (6) ... 0 0,124023438 0,25 0,25 0 0,126953125 0,25 0,125976563 0 x (8) = 1 0,000976563 0,000976563 0,000976563 0,000976563 = 0,000976563 < 10 3 Trang 29 Vậy nghiệm gần đúng của hệ ph ơng trình là: x1 0,624023438 x 0,374023438 2 (8) =x = x3 0,124023438 0,125976563 x4 Trang 30 CHNG IV NI SUY VA XP X HAM A TểM TT Lí THUYT: 4.1 t bi toỏn: (4.1) Vi n l sụ t nhiờn... x 0 : N (1) ( x ) = y0 + f [ x0 , x1 ] ( x x0 ) + f [ x0 , x1 , x2 ] ( x x0 )( x x1 ) 2 Tính tỉ sai phân cấp 1 của f(x): [ x0 , x1 ] = [ 0,0;0,3] f [ x0 , x1 ] = y1 y0 1,132647 1 = = 0,442157 x1 x0 0,3 0 [ x1 , x2 ] = [ 0,3;0,6 ] f [ x1 , x2 ] = y2 y1 0,754338 1,132647 = = 6,28995 x2 x1 0,6 0,3 Tính tỉ sai phân cấp 2 của f(x): [ x0 , x1 , x2 ] = [ 0,0;0,3;0,6 ] f [ x0 , x1 , x2 ] = f... x ) = y0 + f [ x0 , x1 ] ( x x0 ) + f [ x0 , x1 , x2 ] ( x x0 )( x x1 ) 2 Trang 35 Tính tỉ sai phân cấp 1 của f(x): [ x0 , x1 ] = [ 2,2;2,4 ] f [ x0 , x1 ] = y1 y0 0,767844 0,709267 = = 0,292885 x1 x0 2,4 2,2 [ x1 , x2 ] = [ 2,4;2,6 ] f [ x1 , x2 ] = y2 y1 0,816609 0,767844 = = 0,243825 x2 x1 2,6 2,4 Tính tỉ sai phân cấp 2 của f(x): [ x0 , x1 , x2 ] = [ 2,2;2,4;2,6 ] f [ x0 , x1 , x 2