Gauss: zitsanzo za njira ndi milandu wapadera

Gauss njira umatchedwanso njira stepwise Kupha zosintha sakudziwika dzina la otchuka German wasayansi KF Gauss, adakali moyo analandira udindo zosavomerezeka "Mfumu ya masamu." Komabe, njira imeneyi kudziwika yaitali asanabadwe chitukuko European, ngakhale m'zaka za m'ma Ine. BC. e. Ancient akatswiri Chinese kuti ntchito m'mabuku ake.

Gauss ndi njira yakale kuthetseratu machitidwe a maikwezhoni liniya algebraic (Slough). Ndi abwino njira mwachangu mawerengetsedwe zochepa kukula.

The njira yokha tichipeza chimachititsanso awiri: patsogolo ndi kuigonjetsa. Direct Inde otchedwa akuyambira wasonyeza SLAE triangular mawonekedwe, mwachitsanzo ziro phindu pansi waukulu opendekera. Anabweza ikukhudza kupeza nthaŵi zosintha, kusonyeza aliyense variable kudzera m'mbuyomo.

Phunzirani kugwiritsa ntchito kuchita, Gauss basi zokwanira kudziwa malamulo yaikulu ya chulutsa, Kuwonjezera ndi wochotsera a manambala.

Pofuna kuonetsa aligorivimu kwa kuthetsa machitidwe liniya njira imeneyi, ife kufotokoza chitsanzo chimodzi.

Choncho, atha ntchito Gauss:

× + 2y + 4z = 3
2X + 6y + 11z = 6
4x-2y-2z = -6

Tiyenera wachiwiri ndi wachitatu mizere kuti lichotse × variable. Kuti izi ife kuwonjezera kwa iye woyamba kuchulukitsa ndi -2, ndi -4, motero. ife kupeza:

× + 2y + 4z = 3
2y + 3z = 0
-10y-18z = -18

Tsopano mzere 2 kuchulukitsa ndi 5 ndi kuwonjezera kwa wachitatu:

× + 2y + 4z = 3
2y + 3z = 0
-3z = -18

Sitinatenga dongosolo yathu mawonekedwe triangular. Tsopano timachita iwowo. Timayamba ndi mzere womalizira:
-3z = -18,
z = 6.

Mfundo yachiwiri:
2y + 3z = 0
2y + 18 = 0
2y = -18,
Y = -9

Mfundo yoyamba:
× + 2y + 4z = 3
x-18 + 24 = 3
× = 18-24 + 3
× = -3

M'malo mfundo za zosintha mu deta pachiyambi, ife kutsimikizira kulondola mlandu.

Mwachitsanzo izi zikhoza kuthetsedwa zambiri oloŵa m'malo mwa wina aliyense, koma yankho akuyenera kukhala yemweyo.

Pa nthawi imene nyengo otsogolera mzere woyamba imakonzedwa ndi mfundo zazing'ono kwambiri. Si mantha koma m'malo complicates kuwerengetsera lapansi. The njira yothetsera Gauss ndi pivoting pa mzati. Kwenikweni ake ali motere: mzere woyamba wa pazipita adafunafuna modulo amafotokozera, ndime imene ili, kusintha malo ndime 1, kuti mfundo yathu pazipita amakhala chinthu choyamba waukulu opendekera. Chotsatira ndi muyezo mawerengedwe ndondomeko. Ngati ndi kotheka, ndondomeko chimasintha mizati m'madera ena Mungathe kubwereza.

Baibulo lina njira ndi njira Gauss Gauss-Jordan.

Izo ntchito pothetsa machitidwe liniya lalikulu, pamene osiyanitsidwa masanjidwewo ya masanjidwewo ndi udindo (nambala ya mizere nonzero).

Akamanena za njira izi ndi dongosolo choyambirira osandulika, mwa kusintha mu masanjidwewo adzadziwire ndi zina kupeza zosintha.

The aligorivimu ndi kuti:

1. dongosolo la maikwezhoni, monga mwa njira Gauss, ndi triangular mawonekedwe.

2. mzere lililonse lagawidwa nambala yeniyeni mu njira yakuti unit chasanduka pa waukulu opendekera.

3. Mfundo yomaliza kuchulukitsa ndi nambala inayake ndi subtracted ku penultimate kotero kuti kufika pa waukulu opendekera 0.

4. Khwerero 3 akubwerezedwa sequentially kwa mizere onse mpaka pamapeto pake osati kupanga unit masanjidwewo.