Chislennoe reshenie lineynykh integral'nykh uravneniy: Primenenie predobuslavlivateley dlya povysheniya skorosti skhodimosti ite,Used

Chislennoe reshenie lineynykh integral'nykh uravneniy: Primenenie predobuslavlivateley dlya povysheniya skorosti skhodimosti ite,Used

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Brand: LAP Lambert Academic Publishing
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Integral'nye uravneniya v sovokupnosti s chislennymi metodami ikh resheniya yavlyayutsya moshchnym sredstvom issledovaniya razlichnykh zadach iz takikh oblastey matematicheskoy fiziki, kak teoriya uprugosti, akustika, gidrodinamika, elektrodinamika. Chislennoe reshenie lineynogo integral'nogo uravneniya vtorogo roda proizvoditsya putem konechnomernoy approksimatsii sistemoy lineynykh algebraicheskikh uravneniy. V sluchae, esli obuslovlennost' poluchennoy sistemy vysoka, skhodimost' iteratsionnykh metodov ee resheniya okazyvaetsya ochen' medlennoy. Eto mozhet ne sostavlyat' vazhnosti v razovykh vychisleniyakh, odnako stanovitsya aktual'nym, kogda trebuetsya mnogokratnoe reshenie uravneniya. Tak byvaet, k primeru, pri reshenii obratnykh zadach ili v sluchae resheniya nelineynykh uravneniy s ispol'zovaniem linearizatsii. Dlya ponizheniya obuslovlennosti sistemy vypolnyaetsya ee podgotovka putem umnozheniya na vspomogatel'nuyu matritsu (predobuslavlivatel', preconditioner), obladayushchuyu svoystvami, v chemto blizkimi k svoystvam obratnoy matritsy sistemy. V rabote rassmatrivayutsya predobuslavlivateli, orientirovannye na chislennoe reshenie lineynykh integral'nykh uravneniy vtorogo roda i osnovannye na idee gruboy approksimatsii obratnogo operatora.

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