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Chislennoe reshenie lineynykh integral'nykh uravneniy: Primenenie predobuslavlivateley dlya povysheniya skorosti skhodimosti iteratsionnykh metodov (Russian Edition) - Softcover

 
9783848427956: Chislennoe reshenie lineynykh integral'nykh uravneniy: Primenenie predobuslavlivateley dlya povysheniya skorosti skhodimosti iteratsionnykh metodov (Russian Edition)
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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 chem-to 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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Fedotov Il'ya Evgen'evich, kandidat fiziko-matematicheskikh nauk, dotsent MGTU MIREA, Moskva.

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Book Description Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Integral'nye urawneniq w sowokupnosti s chislennymi metodami ih resheniq qwlqütsq moschnym sredstwom issledowaniq razlichnyh zadach iz takih oblastej matematicheskoj fiziki, kak teoriq uprugosti, akustika, gidrodinamika, älektrodinamika. Chislennoe reshenie linejnogo integral'nogo urawneniq wtorogo roda proizwoditsq putem konechnomernoj approximacii sistemoj linejnyh algebraicheskih urawnenij. V sluchae, esli obuslowlennost' poluchennoj sistemy wysoka, shodimost' iteracionnyh metodow ee resheniq okazywaetsq ochen' medlennoj. Jeto mozhet ne sostawlqt' wazhnosti w razowyh wychisleniqh, odnako stanowitsq aktual'nym, kogda trebuetsq mnogokratnoe reshenie urawneniq. Tak bywaet, k primeru, pri reshenii obratnyh zadach ili w sluchae resheniq nelinejnyh urawnenij s ispol'zowaniem linearizacii. Dlq ponizheniq obuslowlennosti sistemy wypolnqetsq ee podgotowka putem umnozheniq na wspomogatel'nuü matricu (predobuslawliwatel', preconditioner), obladaüschuü swojstwami, w chem-to blizkimi k swojstwam obratnoj matricy sistemy. V rabote rassmatriwaütsq predobuslawliwateli, orientirowannye na chislennoe reshenie linejnyh integral'nyh urawnenij wtorogo roda i osnowannye na idee gruboj approximacii obratnogo operatora. 160 pp. Russisch. Seller Inventory # 9783848427956

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