Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (/) od 3: Sos SPA deg Tekk Dekomposs U A. Prsp Dekomposs U d Idetts trks [A] dr SPA ddekomposs (dfktorsss) mejd mtrks-mtrk segtg wh () d segtg ts (U) sedemk rp sehgg dettsy dh: [A] [] [U] t A U B. Nots trks U erdsrk etode Dootte Nots mtrks sepert d ts dtsk s: 2 2 2 2 Perhtk hw sem eeme dgo dr mtrks d ts erhrg (st)! Nots mtrks U dtsk s: U 2 2 22 2 Perhtk hw sem eeme yg teretk d wh
Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (2/2) dgo dr mtrks U d ts ( ) erhrg (o)! C. Nots trks U erdsrk etode Crot Nots mtrks sepert d ts dtsk s: 2 2 2 22 2 Perhtk hw sem eeme dgo dr mtrks d ts tdk hrs erhrg (st) sedgk eeme-eeme d ts dgo semy erhrg (o)! Nots mtrks U dtsk s: U 2 2 2 Perhtk hw sem eeme dgo ( ) erhrg (st) sedgk yg teretk d why erhrg (o)! D. Nots trks A d U dm SPA Nots trks U seg dekompos mtrks A dpt dtsk dm SPA s: [A] [] [] [U] [] []
Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (3/3) Sehgg dm ots etode Dootte dpt dtsk: 2 22 2 2 2 2 2 2 Sedgk dm ots etode Crot dpt dtsk: 2 22 2 2 2 2 2 2 E. Deskrps Thp d Strteg Dekomposs Nots A U dm etode Dootte sepert d ts dpt drk dm opers perk mtrks (seg cotoh: mtrks ) s: Brs ( ): ; 2 2 K Brs 2 ( 2): 2 2 22 2 2 22 23 2 3 23 2 2 2
Brs 3 ( 3): 3 3 32 3 2 32 22 33 3 3 32 23 33 3 3 32 2 3 Brs ( ): 2 2 2 22 3 3 2 23 3 33 - - 2 2-3 3- - -- 2 2 3 3 # Dr opers-opers perk mtrks U sepert d ts dpt dsmpk eerp h erkt: (). eksme proses dekomposs dkk deg cr megs tereh dh rs pertm mtrks U. Sejty megs mtrks pd rs teredh tereh d (m rs ke-2) d kemd dkt pegs mtrks U pd rs yg sm demk setersy smp rs terkhr (ke-). (2). Hrg-hrg dr sem eeme mtrks U pd rs detk deg eeme-eeme mtrks A (mtrks s) (3). Hrg-hrg eeme pd koom tk mtrks dpt dhtg meggk persm erkt: / ; 2 (4). Jmh mksmm opers pejmh per eeme mtrks A ses deg jmh/poss rs (5). Pd rs redh gkh/ters pegs mtrks U eh yk ddgk deg mtrks d seky. Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (4/4)
Tgs/th: kk h yg sm sepert d ts tk kofgrs mtrks U yg dss deg etode Crot! F. Agortm Dekomposs d Kompts Prkts (). Agortm sos merk deg etode Dootte: Brs : ; Brs 2: Pegs mtrks : 2 2 Pegs mtrks U: 22 22 2 2 23 23 2 3 24 24 2 4 Brs 3: 2 2 2 Pegs mtrks : 3 3 ( 32 3 2 ) 32 22 Pegs mtrks U: 3 33 3 3 3 32 23 34 34 3 4 32 24 3 3 3 32 2 Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (5/5)
Brs : Pegs mtrks : 2 3 ( ) 2 22 2 ( ) 3 3 33 2 23 ( ) 2 2 Pegs mtrks U: 2 2 (). Agortm sos merk deg etode Crot: Se th co sdr kk sedr deg cr megkt gh-gkh tk etode Dootte sepert d ts deg cermt d seksm! (c). Kompts deg Fortr-77 tk etode Dootte: DE VARIABE ATRIKS (2-dmes): C PRGRA Pegj Dekomposs U C Dekrs Jes d Vre: C ----------------------------- IPICIT NNE INTEGER rg PARAETER (rg 7) INTEGER jeq REA*8 A(rgrg)U(rgrg) C U(rgrg) CA system('cer') C Proses Pemsk Hrg Vre: C -------------------------------- WRITE(*) 'Jmh Persm : ' READ(**) eq D eq Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (6/6)
D j eq WRITE(*2) 'A('''j') : ' READ(**) A(j) C Proses Pemgg Sprogrm Ems Gss-Jord: C ----------------------------------------------------- CA DECU(eqAU) C Pempr/peyj Hs Perhtg: C -------------------------------------- WRITE(*3) 'trks U yg dperoeh:' D eq D j eq WRITE(*4) U(j) WRITE(**) FRAT (3XA$) 2 FRAT (3XAIAIA$) 3 FRAT (/XA) 4 FRAT (3XF.4$) C 4 FRAT (3XF.43XF.43XF.43XF.43XF.4) STP END SUBRUTINE DECU(AU) C --------------------------------------------------------------------------- C SUBPRGRA DEKPSI U: C erpk sos DEKPSISI trks A mejd mtrks-mtrks C d U deg formt [A] [].[U] yg hsy dsmp dm U C dmes mtrks A (detk deg jmh PA) C A mtrks jr sgkr yg ers koefse persm C U mtrks jr sgkr tempt peymp hs dekomposs C mtrk A mejd d U (yg dsmp sekgs dm U). C --------------------------------------------------------------------------- C Dekrs Vre: C ------------------- INTEGER REA*8 A(77)U(77) INTEGER jk REA*8 sm C Proses pegs mtrks d U (dm mtrks U): C ---------------------------------------------------- D j C Proses pegs mtrks U pd rs pertm: C ---------------------------------------------- U(j) A(j) D 2 C Proses pegs mtrks : C --------------------------- U() A()/U() sm.d D j 2- D k -2 sm sm U(k)*U(kj) U(j) (A(j) - sm)/u(jj) Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (7/7)
C Proses pegs mtrks U: C --------------------------- D j sm.d D k - sm sm U(k)*U(kj) U(j) A(j) - sm RETURN END DE VARIABE VEKTR (2-dmes): C C C PRGRA Sos Sstem Persm Ajr er (SPA) t t Persm Ajr er Smt deg tekk TRIDIAGNA yg terwk (dsmp) dm vektor C Dekrs Jes d Vre: C ----------------------------- IPICIT NNE INTEGER rg PARAETER (rg 7) INTEGER eq REA*8 (rg)d(3*rg)(rg) CA system('cer') PEN (FIE's3dg.dt') C Proses Pemsk Hrg Vre: C -------------------------------- READ(*) eq WRITE(**) 'Jmh Persm : 'eq READ(*) d(eq)d(2*eq)() D 2eq- READ(*) d()d(eq)d(2*eq)() READ(*) d(eq)d(eqeq)(eq) C Proses Pemgg Sprogrm Ems Gss-Jord: C ----------------------------------------------------- CA V3DIAG(eqd) C Pempr/peyj Hs Perhtg: C -------------------------------------- WRITE(**) '--------HASI---------' D eq WRITE(*4) '('') '() CSE() 2 FRAT (3XAIAIAG5.7) 3 FRAT (5XAIAG5.7) 4 FRAT (5XAIAG5.7) STP END INCUDE 'v3dg.s' Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (8/8)
Fe v3dg.s (dm cde): SUBRUTINE V3DIAG(d) C --------------------------------------------------------------------------- C SUBPRGRA SUSI ATRIKS TRI-DIAGNA deg EIINASI GAUSS C erpk sos Sstem Persm Ajr er (SPA) deg C formt persm mtrks: [A].[] [] deg rc s C jmh persm jr er (dmes SPA) C d(2..) vektor koefse dgo wh deg dmes - C d(..2) vektor koefse dgo tm deg dmes C d(2..3-) vektor koefse dgo ts deg dmes - C vektor vre persm yg k dcr hrg-hrgy C vektor rs k yg ers hrg-hrg persm tgg C --------------------------------------------------------------------------- C Dekrs Vre: C ------------------- INTEGER REA*8 d(3*)()() INTEGER m REA*8 PIVTUT C Proses sos: () Sstts d Ems C ------------------------------------------- D - PIVT d() UT d()/pivt d() UT d() d() - UT*d(2*) () () - UT*() C Proses sos: () Sstts Bk C ----------------------------------- () ()/d() D -- () (() - d(2*)*())/d() RETURN END (d). Utk Pemhm yg eh medm coh t progrm dm hs Fortr-77 tk etode Crot! G. ft Dekomposs U tk Sos SPA Sos SPA [A] [] [] me tekk dekomposs mtrks [A] sgt ermft tk meyeesk proem-proem tp mode mtemts yg memetk SPA deg mtrks [A] yg sm tk erg vektor jw []. Deg tekk dekomposs U peyees k mejd sgt efse d yk meghemt wkt pd st teh Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (9/9)
dperoeh dekomposs mtrks [A] kre hs dekomposs U terset dpt dpk tk sem SPA deg mtrks [A] yg detk. Betk mm SPA yg meggk mtrks [A] yg detk sepert dsetk d ts dpt dtsk s: [A] 2 2 22 2 2 2 2 22 2 2 Perhtk hw etk d ts sesgghy merpk perk 2 etk mtrks tr mtrks jr sgkr [A] yg erdmes deg mtrk seg 4 yg erdmes m deg hs mtrks yg jg erdmes m! H. Sos Nmerk SPA me Dekomposs U Sprogrm (SUBRUTINE) d wh dpt dgk tk sos SPA deg etk orm: [A] [] [] meggk mtrks U seg hs dekomposs mtrks [A] deg etode Dootte. C PRGRA Sos SPA deg Dekomposs U C Dekrs Jes d Vre: C ----------------------------- IPICIT NNE INTEGER rg PARAETER (rg 7) INTEGER jeq REA*8 U(rgrg)(rg)(rg) CA system('cer') PEN (FIE'ptU.dt') C Proses Pemsk Hrg Vre dr FIE: C ------------------------------------------ READ(*) eq D eq READ(*) (U(j) jeq)() C Proses Pemgg Sprogrm Ems Gss-Jord: C ----------------------------------------------------- CA DECU(eqU) CA SVU(eqU) Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (/)
C Pempr/peyj Hs Perhtg: C -------------------------------------- WRITE(*3) 'trks U d vektor yg dperoeh:' D eq D j eq WRITE(*4) U(j) WRITE(*5) '('') '() CSE() FRAT (3XA$) 2 FRAT (3XAIAIA$) 3 FRAT (/XA) 4 FRAT (3XF.4$) 5 FRAT (5XH 5XAIAG.4) STP END INCUDE 'decou.s' INCUDE 'sovu.s' Tgs! Ujh progrm d ts tk SPA erkt: 2 4 2 3 4 3 7 2 3 28 3 Perhtk deg seksm hs dekompossy (mtrks U) d sos vektor -y! I. Dftr Pstk Atkso Ked E. A Itrodcto to Nmerc Ayss Joh Wey & Sos Toroto pp. 33-39 978. Atkso.V. Hrey P.J. A Itrodcto to Nmerc ethods wth Psc Addso-Wesey Pshg Co. Tokyo pp. 49-59 983. Bsmo Setjo Kmp Bh Kh etode Nmerk Jrs TGP-FTUI 999. Ser Kh etode Nmerk (od 3: Sos SPA deg Tekk Dekomposs U) (/)