EVIEW OPEASI MATIKS T E K N I K L I N G K U N G A N I T B
MENGHITUNG INVES MATIKS
DETEMINAN Hny untuk squre mtries Jik determinn = mtriks singulr, tidk puny invers b d d b d b det det b b b b b b b b b
CAI INVES NYA
SISTEM PESAMAAN LINEA S I M U L T A N E O U S L I N E A E Q U A T I O N S
METODE PENYELESAIAN Metode grfik Eliminsi Guss Metode Guss Jourdn Metode Guss Seidel LU deomposition
METODE GAFIK Det{A} A is nonsingulr so invertible Unique solution -
SISTEM PESAMAAN YANG TAK TESELESAIKAN No solution Det [A] =, but system is inonsistent Then this system of equtions is not solvble
SISTEM DENGAN SOLUSI TAK TEBATAS Det{A} = A is singulr infinite number of solutions 8 Consistent so solvble
ILL-CONDITIONED SYSTEM OF EQUATIONS A liner system of equtions is sid to be illonditioned if the oeffiient mtri tends to be singulr
ILL-CONDITIONED SYSTEM OF EQUATIONS A smll devition in the entries of A mtri, uses lrge devition in the solution...99.8..99.9
GAUSSIAN ELIMINATION Merupkn slh stu teknik pling populer dlm menyelesikn sistem persmn liner dlm bentuk: A X C Terdiri dri du step. Forwrd Elimintion of Unknowns.. Bk Substitution
FOWAD ELIMINATION Tujun Forwrd Elimintion dlh untuk membentuk mtriks koefisien menjdi Upper Tringulr Mtri 8.8..
FOWAD ELIMINATION Persmn liner n persmn dengn n vribel yng tk dikethui... b n n... b n n n n nn n n n b.........
CONTOH 8 8 mtriks input
FOWAD ELIMINATION 8 9 9 9 9 9 9 9 9 9
FOWAD ELIMINATION 9 9 9 9 9 9 9 9 9 9
BACK SUBSTITUTION 9 9
GAUSS - JOUDAN 9 8 8
WANING.. Du kemungkinn keslhn -Pembgin dengn nol mungkin terjdi pd lngkh forwrd elimintion. Mislkn:.99.9 - Kemungkinn error kren round-off (keslhn pembultn)
CONTOH Dri sistem persmn liner.99.9 = Akhir dri Forwrd Elimintion.. =.9.99..
KESALAHAN YANG MUNGKIN TEJADI Bk Substitution.....9999..
CONTOH KESALAHAN Bndung-kn solusi et dengn hsil perhitungn.9999.. X lulted X et
IMPOVEMENTS Menmbh jumlh ngk penting Mengurngi round-off error (keslhn pembultn) Tidk menghindrkn pembgin dengn nol Gussin Elimintion with Prtil Pivoting Menghindrkn pembgin dengn nol Mengurngi round-off error
PIVOTING Eliminsi Guss dengn prtil pivoting mengubh tt urutn bris untuk bis mengpliksikn Eliminsi Guss ser Norml How? Di wl sebelum lngkh ke-k pd forwrd elimintion, temukn ngk mksimum dri: pk k p n, kk, k, k,..., nk Jik nili mksimumny Pd bris ke p, Mk tukr bris p dn k.
PATIAL PIVOTING Wht does it Men? Gussin Elimintion with Prtil Pivoting ensures tht eh step of Forwrd Elimintion is performed with the pivoting element kk hving the lrgest bsolute vlue. Jdi, Kit mengeek pd setip lngkh pkh ngk mutlk yng dipki untuk forwrd elimintion (pivoting element) dlh sellu pling besr
PATIAL PIVOTING: EXAMPLE.9.99 Consider the system of equtions In mtri form.99.9 = Solve using Gussin Elimintion with Prtil Pivoting using five signifint digits with hopping
PATIAL PIVOTING: EXAMPLE Forwrd Elimintion: Step Emining the vlues of the first olumn, -, nd or,, nd The lrgest bsolute vlue is, whih mens, to follow the rules of Prtil Pivoting, we don t need to swith the rows.9.99.... Performing Forwrd Elimintion
PATIAL PIVOTING: EXAMPLE.... Forwrd Elimintion: Step Emining the vlues of the first olumn -. nd. or. nd. The lrgest bsolute vlue is., so row is swithed with row.... Performing the row swp
PATIAL PIVOTING: EXAMPLE Forwrd Elimintion: Step Performing the Forwrd Elimintion results in:....
PATIAL PIVOTING: EXAMPLE Bk Substitution Solving the equtions through bk substitution........
PATIAL PIVOTING: EXAMPLE X et X lulted Compre the lulted nd et solution The ft tht they re equl is oinidene, but it does illustrte the dvntge of Prtil Pivoting
SUMMAY -Forwrd Elimintion -Bk Substitution -Pitflls -Improvements -Prtil Pivoting