Yuav ua li cas los daws kom tau ib tug system ntawm linear equations ntawm lub hom

Rau to taub tag nrho li cas los daws kom tau ib tug kev sib npaug, nws yog tsim nyog los xav txog dab tsi nws nruab nrab yog. Raws li yog tseeb los ntawm cov sij hawm rau nws tus kheej, lub "system" - ib tug sau ntawm ob peb npaug txuam nrog txhua lwm yam. Muaj tshuab ntawm algebraic thiab differential sib npaug. Nyob rau hauv no tsab xov xwm peb yuav tau them nyiaj mloog rau yuav ua li cas los daws kom tau ib tug kev sib npaug ntawm cov thawj hom.
Los ntawm txhais, ib tug algebraic kab zauv yog hu ua, nyob rau saum toj no cov tsiaj ntawv tshwm sim yooj yooj yim xaam ua hauj lwm, i.e. Tsis tas li ntawd, division, sib rho, lej khu, exponentiation , thiab nrhiav lub hauv paus. Ib tug algorithm daws cov kab zauv ntawm no hom yog txo mus rau nws transformation mus los ntawm nws mus nrhiav qhov sib npaug tab sis yooj yim siv.
System of algebraic equations raug muab faib ua linear thiab nonlinear.
Lub system ntawm linear equations (tsiaj ntawv SLAE kuj lug siv) yog txawv los ntawm ib tug system ntawm nonlinear sib npaug uas muaj tsis paub hais tias cov tsiaj ntawv nyob rau hauv thawj degree. General saib SLAE nyob rau hauv matrix daim ntawv zoo li: Ax = b, qhov twg A yog - ib tug ntau yam ntawm lub npe hu yam, x - variables, b - ib tug ntau yam ntawm lub npe hu dawb cov tswv cuab.

Muaj ntau ntau txoj kev yuav ua li cas los daws kom tau ib tug kev sib npaug ntawm hom, lawv muab faib mus rau hauv ncaj qha thiab iterative txoj kev. Direct txoj kev tso cai rau peb mus nrhiav qhov tseem ceeb ntawm ntau yam rau ib tug tej yam muaj pes tsawg tus ntawm zauv transformations thiab iterative algorithm siv successive approximation thiab paub kev cai.

Cia peb xav txog ib qho piv txwv ntawm yuav ua li cas los daws kom tau ib tug system ntawm linear equations siv rau hauv tib neeg txoj kev nrhiav qhov tseem ceeb ntawm lub zog. Qhov ncaj txoj kev muaj xws li txoj kev ntawm Gauss, Jordan-Gauss, Kramer, cheb thiab lwm tus neeg. Ib tug ntawm cov feem ntau yooj yim yuav tsum tau hu ua cov qauv ntawm cov Cramer, feem ntau nws yog nrog nws paub lub matrix pib nyob rau hauv cov ntaub ntawv kawm. Qhov no yog tsim los daws quadratic linear tshuab, piv txwv li xws systems nyob rau hauv uas lub xov tooj ntawm sib npaug yog sib npaug zos rau cov xov tooj ntawm tsis paub hais tias cov tsiaj ntawv nyob rau hauv txoj hlua. Tsis tas li ntawd, nyob rau hauv thiaj li yuav daws tau ib tug kev sib npaug los ntawm Cramer, koj yuav tsum ua kom paub tseeb tias cov dawb cov ntsiab lus - tsis pes tsawg (ib tug prerequisite).

Algorithm daws yog raws li nram no: 1 nyob rau hauv ib tug matrix uas muaj lub npe hu yam thiab tshuab thiab yog nws cov ntsiab determinant ntawm Δh. Lub determinant yog pom los ntawm subtracting cov khoom ntawm lub qhov kab pheeb ces kaum ntsiab ntawm cov khoom hais ntsiab.

Ntxiv tso ua ke 2 matrix uas tus thawj kem ntawm cov kev hloov tseem ceeb muaj ntsiab b, piv rau lub yav dhau los piv txwv yog determinant Δh _1.

Peb tsim lub matrix 3, qhov tseem ceeb ntawm lub coefficients muaj kev hloov rau tus thib ob kem, peb pom tias lub determinant ntawm tus matrix Δh _2. Thiab yog li ntawd nyob rau hauv kom txog thaum, kom txog thaum koj xam cov determinant ntawm tus matrix, qhov twg lub coefficients b yog nyob rau hauv rau kem tom kawg.

Yuav kom nrhiav tau tus nqi ntawm ib qho kev nce mus nce los, koj yuav tsum tso cov coefficients tau los ntawm hloov qualifiers muab faib mus rau hauv lub ntsiab determinant, piv txwv li ₁ = x Δh ₁ / Δh, ₂ x ₂ = Δh / Δh etc.
Yog hais tias koj muaj lus nug txog yuav ua li cas los daws kom tau ib tug kev sib npaug nyob rau hauv ib txoj kev kom koj siv thiab kev cob qhia cov ntaub ntawv, uas ntxaws tag nrho cov yooj yim cov kauj ruam.