Kugadzirisa kwegadziriro Linear equations ari mhando

Nokuti kunzwisisa sei kugadzirisa kwegadziriro equations kwakakwana, zvakakodzera kufunga rinomiririra. Sezvo zviri pachena kubva rokuti pacharwo, "mamiriro" - dzakaunganidzwa equations akawanda chokuita nomumwe. Kune mugadziriro algebraic uye differential equations. Munyaya ino tichashandisa kuteerera sei kugadzirisa kwegadziriro equations wokutanga mhando.
By tsanangudzo, imwe algebraic mukana wokuti vanhu vanga anonzi, makavigwa pamusoro variables kuitika chete nyore kwemasvomhu kushanda, i.e. Uyezve, nokupesana, kubvisa, chokuwanziridza, Exponentiation , uye kuwana mudzi. An algorithm nokuti nekugadzirisa mukana wokuti vanhu vanga kwakadai ipfupi kwayo shanduko kuburikidza nawo kuwana vakaenzana asi nyore kuvaka.
System pamusoro algebraic equations akakamurwa Linear uye nonlinear.
The maitiro pamusoro Linear equations (chidimbu SLAE akashandisawo nevakawanda) rakasiyana kwegadziriro nonlinear equations kuti pane vasingazivikanwi variables rokutanga dhigirii. General maonero SLAE mu chizvaro muchimiro sokunge: Ax = b, apo A iri - siyana anozivikanwa zvinhu, X - variables, b - siyana anozivikanwa vakasununguka nhengo.

Pane zvakawanda sei kugadzirisa kwegadziriro equations iyi mhando, ivo rakakamurwa zvakananga uye iterative nzira. Direct nzira inotipa kuwana zvinokosheswa variables kuti imwe nhamba kwemasvomhu transformations uye iterative algorithm kushandisa anotevedzana rakada uye kunatsiridzwa.

Ngatimbokurukurei muenzaniso sei kugadzirisa kwegadziriro Linear equations uchishandisa zvakananga nzira yokuwana tsika yacho variables. The yakananga nzira zvinosanganisira nzira Gauss, Jordan-Gauss, Kramer, kutsvaira uye nevamwe. Chimwe chezvinhu nyore anganzi nzira pakati Cramer, kazhinji zvakanga naye kujairirana chizvaro kunotangira hweutungamiri. Nzira iri rakagadzirirwa nekugadzirisa quadratic Linear enyika, kureva hurongwa hwakadaro umo nhamba equations akaenzana nokuwanda asingazivikanwi variables iri tambo. Uyewo, kuti kugadzirisa kwegadziriro equations kubudikidza Cramer, unofanira kuva nechokwadi chokuti vakasununguka mashoko - kwete razero (a chinodiwa).

Algorithm anogadzirisa sezvinotevera: 1 ari chizvaro raiumbwa anozivikanwa zvinhu uye hurongwa uye zviri zvayo chikuru determinant pakati Δh. The determinant inowanikwa kuburikidza Tikabvisa zvibereko yechipiri diagonal zvinhu chigadzirwa zvinhu huru.

Uyezve akaanyora 2 chizvaro apo mbiru okutsiva tsika iripo okunze b wokutanga, saizvozvowo yapfuura muenzaniso uri determinant Δh _1.

We vanoumba chizvaro 3, tsika yacho coefficients iripo kutsiva yechipiri mbiru, tinoona kuti determinant kuti chizvaro Δh _2. Nezvimwewo kusvikira, kusvikira iwe ngaaverenge determinant pakati chizvaro, apo coefficients b vari vokupedzisira mbiru.

Kuti uwane kukosha imwe shanduka, unofanira kusunungura coefficients yaunganidzwa dzinomiririra qualifiers akakamurwa huru determinant, kureva ₁ = X Δh ₁ / Δh, ₂ X ₂ = Δh / Δh etc.
Kana uine mibvunzo pamusoro sei kugadzirisa kwegadziriro equations neimwe nzira kukukurudzira kuti bhuku uye kudzidzisa zvinhu, izvo detailed dzinokosha nhanho dzose.