Kule ncwadi, sizocabangela ukuthi iyini indlela yesiGaussian, kungani idingeka, nokuthi siyini isimiso sayo. Sizophinde sibonise sisebenzisa isibonelo esisebenzayo ukuthi indlela ingasetshenziswa kanjani ukuxazulula uhlelo lwezibalo zomugqa.
Incazelo yendlela ye-Gauss
Indlela ye-Gauss indlela yakudala yokususa okulandelanayo kokuguquguqukayo okusetshenziselwa ukuxazulula . Iqanjwe ngesazi sezibalo saseJalimane uCarl Friedrich Gauss (1777-1885).
Kodwa okokuqala, masikhumbule ukuthi i-SLAU ingakwazi:
- ube nesixazululo esisodwa;
- ube nenani elingapheli lezixazululo;
- zingahambelani, okungukuthi zingabi nezixazululo.
Izinzuzo ezingokoqobo
Indlela ye-Gauss iyindlela enhle yokuxazulula i-SLAE ehlanganisa izibalo zomugqa ezingaphezu kwezintathu, kanye namasistimu angewona isikwele.
Isimiso sendlela ye-Gauss
Indlela ihlanganisa lezi zinyathelo ezilandelayo:
- Qondile – i-matrix augmented ehambisana nesistimu yezibalo, incishiswa ngendlela engenhla kwemigqa ibe ifomu elingunxantathu (elinyathelwe), okungukuthi ngaphansi kwediagonal eyinhloko kufanele kube nezakhi ezilingana noziro kuphela.
- emuva - ku-matrix ewumphumela, izakhi ezingenhla kwe-diagonal eyinhloko nazo zisethelwe ku-zero (ukubuka kukanxantathu ophansi).
Isibonelo sesixazululo se-SLAE
Masixazulule isistimu yezibalo zomugqa ngezansi sisebenzisa indlela ye-Gauss.
Isixazululo
1. Okokuqala, sethula i-SLAE ngendlela ye-matrix eyandisiwe.
2. Manje umsebenzi wethu uwukusetha kabusha zonke izakhi ngaphansi kwe-diagonal eyinhloko. Izenzo ezengeziwe zincike ku-matrix ethile, ngezansi sizochaza lezo ezisebenza esimweni sethu. Okokuqala, sishintshanisa imigqa, ngaleyo ndlela sibeka izici zabo zokuqala ngokulandelana okukhuphukayo.
3. Khipha emgqeni wesibili kabili kowokuqala, futhi kowesithathu - kathathu kowokuqala.
4. Faka umugqa wesibili emugqeni wesithathu.
5. Khipha umugqa wesibili emgqeni wokuqala, futhi ngesikhathi esifanayo uhlukanise umugqa wesithathu ngo -10.
6. Isigaba sokuqala sesiphelile. Manje sidinga ukuthola izakhi ezingenalutho ngaphezu kwe-diagonal eyinhloko. Ukuze wenze lokhu, susa okwesithathu kuphindwe ngo-7 emgqeni wokuqala, bese wengeza owesithathu ophindwe ngo-5 kuye wesibili.
7. I-matrix yokugcina enwetshiwe ibukeka kanje:
8. Ihambisana nohlelo lwezibalo:
Impendulo: impande ye-SLAU: x = 2, y = 3, z = 1.