Indlela yokusombulula inkqubo quadratic linear lohlobo

Kuba ukuqonda ngokupheleleyo ukuba yokusombulula inkqubo zibalo, kubalulekile ukuqwalasela ukuba limele ntoni. Njengoko kucacile ukusuka kwikota ngokwawo, i "inkqubo" - ingqokelela quadratic eliqela enxulumene kunye nabanye. Kukho iinkqubo ze-aljibra kunye umehluko zibalo. Kweli nqaku siza kuqwalasela ukuba yokusombulula inkqubo kwizibalo yohlobo lokuqala.
Xa inkcazelo, lenxaki aljibra kuthiwa, apho izinto ngasentla kwenzeka imisebenzi kuphela elula zemathematika, ngamanye Ukongeza, icandelo, ngokuthabatha ngokuphindaphinda, exponentiation , kwaye sifumane ingcambu. Algorithm ukusombulula inxaki yale hlobo liye lancitshiswa inguqu walo ngayo ukufumana ulwakhiwo elingana kodwa lula.
System kwizibalo aljibra zahlulwe zibe kumgama owazisayo kunye nonlinear.
Inkqubo ye quadratic yomgama (shunqulelo SLAE kwakhona isetyenziswa ngokubanzi) wahlukile ukusuka inkqubo quadratic nonlinear ukuba kukho izinto ezingaziwayo kwinqanaba lokuqala. Jikelele view SLAE kwifomu matrix Kubonakala ngathi: Ax = b, apho A yi - ezahlukeneyo izinto aziwayo, x - variables, b - iintlobo ngeentlobo yamalungu ezamahala ezaziwayo.

Kukho iindlela ezininzi zokusombulula njani inkqubo kwizibalo ze olu hlobo, kodwa yahlulwe iindlela ngqo kunye iterative. iindlela ngqo ukuba sikwazi ukufumana amaxabiso kweziganga kwinani elithile utshintshwano zemathematika kunye algorithm yamanyathelo ohlukileyo athatyathiweyo usebenzisa kelelo ezilandelelanayo kunye nokuphuculwa.

Makhe sihlolisise umzekelo yokusombulula njani inkqubo quadratic kumgama owazisayo usebenzisa indlela ngqo ukuba ngokufumana amaxabiso yezahlukileyo. Iindlela ngqo ziquka iindlela GAUSS, Jordan-GAUSS, Kramer, engacimekiyo kunye nabanye. Enye kakhulu elula ekunokuthiwa indlela Cramer, ngokuqhelekileyo ke waba naye nolwazi isizalo iqala ezikwikharityhulam. Lendlela yenzelwe ukuxazulula iinkqubo linear equation, ie iinkqubo ezinjalo apho inani kwizibalo lilingana nenani variables ezingaziwayo ngomtya. Kwakhona, ukuze yokusombulula inkqubo kwizibalo yi Cramer, kufuneka uqinisekise ukuba imigaqo free - hayi zero (a kuyimfuneko).

Algorithm isisombululo ngolu hlobo lulandelayo: 1 matrix eyenziwa iimeko ezaziwayo kunye neenkqubo kwaye onefuthe yayo ephambili Δh. Le onefuthe sifumaneka ngokuthabatha imveliso ye elements zasesekondari idiagonal izinto mveliso main.

Ngaphezu koko zahlanganiswa 2 matrix apho kwikholam yokuqala lwamaxabiso endaweni ezikhoyo izinto b, ngokufanayo ukuya umzekelo edlulileyo onefuthe Δh _1.

Thina ukwenza matrix 3, amaxabiso okuza indawo ezikhoyo kwikholam yesibini, sifumanisa ukuba onefuthe ngayo isizalo Δh _2. Kwaye njalo kwi de, ude ubale onefuthe ngayo isizalo, apho okuza b ezi kwikholam yokugqibela.

Ukuze ufumane ixabiso ethile variable, kufuneka ube uyayikhulula i okuza ezifunyenwe izichazi esikhundleni yahlulwe lo onefuthe omkhulu, ie ₁ = x Δh ₁ / Δh, ₂ x ₂ = Δh / Δh njl
Ukuba unemibuzo malunga yokusombulula indlela inkqubo kwizibalo ngandlel 'ithile sikukhuthaza ukuba ireferensi kunye nezinto zoqeqesho, leyo ucacisiwe onke amanyathelo ezisisiseko.