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Te e eee, c oee AOP epec epo ce coa opoc. He oppoa o a, o oy 80-x oo oa cya pe ay cyeceo eac o cpae c 60- popecc papaoe epcoax oepo cyeceo pay pa ceoo cepepoa, aaac pa cex eoo oepoa. cyccee epoe ce caoc acco yeee epe cox ooo poa cae pae aye c.

ocee 10 e oaeoac y co, e ooee ee aeo cceoa. epoe x oee RBF-cee, oaxc oe poco, e coepae peypc, acpoe [16]. Bopoe peee A pepo ce pooo apxeyp, coepae e oa aaox y epoo cpoo co [17].

ooe ae yeoc ae oaaecy yepcaoc epox cee pee aa apoca pooo y c o cee ooc. B [1819] o ceao cee epepooo a c coa aao y, [20] RBF-cee.

Paccop poeypy pepo RBF-ce (c. Pc.12), ocyece apoca y, aao eo e aopo aoo, a oa ocaa [16].

yc V oeco xoo ce, H oeco epoo cpoo co, Z oeco xoo ce.

peoo, o paep Q aopa pepoox aoo e co e o ao paee ocaoo papeeo pocpace xox cao ce X=(X1, X2, , XV).

Pc. 12. acceca RBF-ce Cem xapamepuyemc mpe ocoeocmu: 1) eucme cpm co; 2) moo epo cpmoo co uem euey amuauoy yu; 3) cuanmuecue eca cex epoo cpmoo co pa euue.

Bee ceye ooae:

c = (c1,c2,...,cV ) eop oopa epa aaoo y epoa cpoo co;

pa oa aaoo y j-o epoa cpoo co;

j V (X - -c ) 2 j j j=f (X,c)= e- X-c 2 = e paao-cepa aaoa y epoa cpoo co;

wij ec c ey i- epoo xooo co j- epoo cpoo co.

Ce oyee ce ae ce p aa, oeee cey aopo.

Aop cea RBF-ce 1. Bepe paep cpoo co H pa oecy pepoox aoo Q. Caece eca epoo cpoo co pe pa 1.

2. Paec ep aaox y epoo cpoo co oax pocpaca xox cao ce, omope xom aop mpeupoox aoo : c = X, j = 1, H.

j j 3. Bepe p oo aaox y epoo cpoo co, j = 1, H ocmamoo o, o a, o o e aaj ac py a pya pocpace xox cao ce.

4. Opee eca epoo xooo co ce wij, i=1, Z j = 1, H.

oo pe ce ec aop pepoox aoo. Bxo i-o epoa xooo co p-o aoa ye pae:

Yi = wi1 f (X,c1)+ wi2 f (X,c2)+... + wiH f (X,cH )= p p p (5) = wi1 f (X,X1)+ wi2 f (X,X2)+... + wiH f (X,XH )= Di.

p p p Pacca o ypaee cex xoo ce cex aoo, oy ceyee ypaee apo ope:

wT = D, (6) f11... f1H f21... f2H e = epooa apa,.....

fH1... fHH fij = f (Xi,X );

j w11... w1Z w =... apa xox caecx eco;

wH1... wHZ D11... D1Z D =... apa xox aoo.

DH1... DHZ Peee wT = -1D (7) ac a coe ae xox caecx eco, oeceae poxoee epooo oepxoc epe pepooe ao pocpace xox cao ce.

Oa apoca oax xooo pocpaca, e coaax c epa aaox y, ac o oo, acoo yao pa p oo, aeao oeco pepoox aoo cooc yoaoo peopaoa.

coae, poeypa acpo caecx eco ec aeo e eceo e ocee poeo, cpeaec p oye ce. ya a oee co opoco ocaec oppoae aopa pepoox aoo, aeao ocaeo paccapaeoe yoaoe peopaoae. o poee ee epec ceyx paeax.

3. A+HC = HOBA APAMA B PABEH accece eo cea cce ypae apyc a xopoo pao aapae epo-epeaoo cce, coao Hoo ooo pexco e aa. Hepoe ce peca coo aepaoe, cyecyee ceo ecoo e, apaee eop aoaecoo ypae, peaaee o coco opae peopaoa eceoc, oopo oo oapy cxoe, pae ep c acceco apao.

pooee epeax ypae eop aoaecoo peypoa ca c ea . . Macea (18311879) . A. Bepacoo (18311895) [21]. eo o, o c oea ocpoe . ao apoo a c epoe peyopo copoc pae (1784) o cepe opo oo pooo ea aa-o eop peypoa poco ocycoaa. Oao, c poco ooc apox a yacc aap, ae ox aeco peypoa. o Mace Bepac o oopeeo eaco py o pya c a eopeec aa o cce. Oa cooa eop ax oea, epyy aao o . . apaa*. aca ypae apaa apoo a pa x aoe epeee epe oye ooceo eoopx paoecx ae, Mace Bepac eapoa ypae ooceo oye cceoa yco ycooc coco paoec.

Ta aac ep a pa eop aoaecoo ypae, a pacea accecx eoo aaa. pooac o ooo oo o 40-x oo aeo ea, o coepaeo ooe e oac o paoopae oxoo. cceoae ycooc, a ae aeca epexox poecco pooa ocaac oco aaa ceo oo epoa.

Tep epoypaee epe oc paoax Bepoca ye 1976 oy, oao peay po o epe HC cepy ypae* ecx aa cpa pao Hapep c coaopa (1989), acoc, [22].

a, cceax ypae HC oy pec e:

epoopoepo;

epoyopo, pyx aecoe oeee oea ypae eo ocax eo oee xapaepc, pyo oaec aeaecoy oepoa (apep, poe e . .).

epoe, o oac cea caocoeo, ce epoopoepa a ae pexcoo poapaeo ce [23].

B aece oea ypae pa epooe oeaeoe eo opoo opa c epeaoo ye a k W =, (8) T s2 + 2Ts +a aece e ypae oaee oeaeoc oea p cyeao xoo oec (ae ocox oeo k=1; T=0,5; =0,1 ypae (8) oopa a, o oeaee coca y oea pae ocaoo oeo - c.

pc. 13).

a) ) Pc. 13. epexoa xapaepca (a) AX () ecooo aecoo oea ypae Oacac peepoo paaa a aao ae cceoa ( cce oaa o paox cxeoexecx pee -peyopo), oa a xo epoopoepa ca o, a ae eo pooy epa, aec, o ce ae ee eee oe x a caaex.

Pc. 14. ep o c epoopoepo, apocpy oe -peyopa Cmpymypa epoompoepa: mpu pempacupyux ya o xoo coe, empe cpmx ya c cuouau amuauou yuu u ou xoo. Ha xoe epo noaemc paocm ey xo oecmue ur u xoo oema x1, ee umepa u npouoa, a a xoe cemu opupyemc ynpaee oecmue u.

B aece poeyp pepo ce cooa A. Aop opaoo pacpocpae o ae ooe o e, o o peye opa o oe a eopo coe HC.

oye ao opa cxee oye eoxoo peycope opae epoyop oea, po oopoo coc peopaoa o a xoe oea xoo ca a xoe epoopoepa, o cyeceo ycoe poeypy pepo.

Pc. 15. peee A acpo apaepo epoopoepa eeec e aop acpaae apaep epoopoepa e o oe ypae u, a o oe xoe oea, cpaa eo c xoo aoo oe. oce ooae cee a pecae o eaeo oee oea, o ec pae peo y e po, o oea pepoox aoo poeype pepo.

cxoa oy 100 xpooco eeppoaac cya opao. a 21 acpoex apaepo ce opoac ec a, a opao, xpoocoa, opya epoopoep eo, pecaa coo 210-papy oceoaeoc oe e. p o, o aao ee aoo apaepo pocpace 21 p o 1 o 1, ecpapoe opoae oeceao cpeoc ee apaepa e xye 0,002.

oce eopoa xpooco eopa epeex oeaac cocooc aoo apaa ce ceoa aoo oe. poepa ocyecac ye oceoaeo oa a ypa xo epoopoepa eoo ooeoo, yeoo eoo opaeoo xooo oec ce cpeeapao o xoo oopa oea a peeo epae o 10 cey. peapeo epeaoa y oea ypae peopaoaac ccey ooex epeax ypae ope o x1 = x2;

(9) = (- 2Tx2 - x1 + kU )/ T.

xeppoae cce ocyecoc c oco ao, pa 0,01 ce. Cyapa oa o ce pe epexo poecca paac aece ep eyaoc ocpy cooaac aee aece oeceoo eca papoa ocoe oy.

pe epexox poecco yeo apaa oy a pax aax oca pecae a pc. 16.

Pc. 16. ye eocppyex oye epoopoepo epexoe poecc a xoe oea ypae pae oe pao A (aae ea cyea): pa 1 aaa oy, 2 oce 2000 ooe, 3 oce 4000 ooe, 4 oce 5000 ooe.

a o oo pcya, o epe pao aopa pee epepo yyac. Beop epeex, ae 5000 ooe, oeceae oe yoeopeoe peee ocaeo aa.

Pc. 17 cppye oeee oea e oo a pepoox aoax, o p poeyox aex ay xooo aa, oopoe oepae yepcaoc apocpyx coc epox cee.

Pc. 17. epexoe poecc CA c oye epoopoepo p ayax xooo aa 1, 0,5; 0; 0,5; 1 (cy epx) Booyec ocy peyao, yco aay. Ha xo opoepa ca oaa e ca o, eo pooy epa, a poco xoy oopay oea a eye peye aax (eo a aepa ca - c. pc. 18).

Pc. 18. Hoa cxea opaa opax ce o [22] oepac ee aoa oe, oopy coppoa eep a peoae AX aaa ypae [24]. Bo pe a ca oe oaae AX c oeo pae peoac o p acoe 0,32 , epoopoep oe ayc, c oo copo, opaa peoace oea oea, a c pyo copo, yca ayy yex oea pe- ocpeoaco oacx, e oc p o c a ey xo xo oea, a ae oa oea oea p acoax, peax acoy cpea eaeo AX (pa 2 a pc. 19).

Ha o pa opoepa o a paa pexcoa ce 3-10-1, . e. c oeco epoo cpo coe pa 10. opeee pooc ce a ee xo oaac cpoa cep apoecx oea pao ay ( aaoe 0,1-1) c acoa 0,16; 0,48; 0,80; 1,11 1,59 .

epaa oa o ce eco epexo poecca, pooeoc oopx, a paee, cocaa 10 cey, paac aece ep yceoc ypae.

Peya cea oaac ya. opoep, apaep oopoo pecae poe 1, cpac c ooe a eo aaa.

aeca AX epoceeo cce ypae pecaea a pc. 19. Oa ocpoea ye a epepo cepe aco, ae aco pepoox cao. o-oy, -a eocaooo paepa cpoo co ce, cepoaa AX a yace 0,61 aeo oaec o aoo. Oao oe, oyee peya ceecye, o cocooc ce ooe oe cooac p cee epoopoepa acoo oac.

Pc. 19. Cepoaa (pa 1) eaea (pa 2) AX cce ypae pecaee pep yeeo oaa cocooc oa yx ox cex exoo eeecx Aopo cyccex Hepox Cee caocoeo pea aay ypae aec oeo paax ooo apa. oeo, a oy opa, cocac a pyoc cepepoa eocpeceo c oeo p acpoe caecx eco epoopoepa, o p coe ooc e aeaeco oe oea, a a, e acoa oce ooco apa. Te oee, o pecaee pep poe ceecy oy oo ooa. Oao o e a, ceye paee poeocppye, o e e exoo coco caocoeo cepoa aeaecy oe aecoo oea oo a ocoa a eo epexox xapaepc.

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