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p ee o 0 o, .e. r 0, 0, W(i ) eec o ye ecoeo ooo payca, oca yo o 0 o (pc. 6.31). pep Haca opypyec cey opao.

Ccea aoaecoo peypoa, epaa paoyo coco, ycoa ayo coco, ec AX paoyo cce c eo ooee ecoeoc e oxaae oy (-1, i0) p ee o 0 o.

a o pc. 6.31, ec paoya ccea ee aca epoo opa, o aya ccea ycoa, a a oa (1, i0) e oxaaec, ec e aca ye opoo opa, o aya ccea eycoa oa (1, i0) oxaaec AX paoyo cce.

ococa pep Haca c:

1) peoc p eecx ypaex eoopx ee paoyo cce;

2) oooc cceoa ycooc cce c aaae.

pep 6.3 cceoa ycooc cce pepe Mxaoa, ec xapaepcecoe ypaee cce ee D(s) = 2s4 + 4s3 + 2s2 + 5s + 1 = 0.

ae s = i, axoc ecea a y Mxaoa:

D(i ) = 2(i )4 + 4(i )3 + 2(i )2 + 5(i ) + 1, oya U() = 24 22 + 1;

V() = (42 + 5).

oopa Mxaoa opae a pc. 6.32. Eo aa oaae, o ccea eycoa. Ec cooa cece, o U() = 0; V() = 0.

Peee x ypae ae: 21,3 = 1 i; 0 = 0; 2,4 = .

Pc. 6.32 oopa Mxaoa pepy 6.Ta a ec oeco-copee op, o ccea eycoa.

pep 6.4 cceoa ycooc cce aoaecoo peypoa (pc.

6.33), ec W1(s) = ; W2(s) = e-2s.

Pc. 6.33 Cpyypa cxea ACP B paoyo coco ccea aoaecoo peypoa ycoa.

Ayo-aoa xapaepca paoyo cce acaec:

opaea a pc. 6.34.

Pc. 6.34 AX paoyo cce pepy 6.Ta a ayo-aoa xapaepca paoyo cce e oxaae oy c oopaa (1, i0), o aya ccea ycoa.

6.8.4 peee pepe cceoa ycooc cce Cpaee paccopex pepe ycooc ooe cea cey o ooceo x peoc.

pep ycooc ypa eecoopao pe, oa xapaepcecoe ypaee ee cee e e epex (n < 4).

pep ycooc Payca ae cp oe p ceo aax oeax, eecoopao ooac, oa n > 4.

pep ycooc Mxaoa eecoopao pe p cceoa cox oooypx cce, oa eoxoo c e ee cpyyp cce cpec caa a ee ycooc.

pep ycooc Haca eecoopao pe p cceoa cox cce. o pep oaaec eceo pe, oa ac ce xapaepc oex eeo cce aa cepeao, pe p aae cce, ocaex aaec y.

oo coeo poo aae acoe pep ycooc oy cooa oe apaepo cce a ee ycooc.

Ha pc. 6.35 opae oopa Mxaoa ycoo cce. Opeo OMpae ae eopa D(i ) (6.35) p = 0 pae ae oea an xapaepcecoo ypae.

Moo oaa, o oe yce cce e oo a coo e an xapaepcecoo ypae. ooy p eo yee ye yeac oo oe an, o cyae Pc. 6.35 oopa Mxaoa ycox cce 3-o opa Pc. 6.36 Cpyypa cxea cce c pe e ce eop D(i ) oya oaooe ooeoe eceoe ppaee, c pa Mxaoa e eopa epeaec apao, apep, ooe 1 ooee 2 (pc. 6.35). Ec yea oe yce ae, o p eoopo eo peeo ae oopa Mxaoa poe epe aao oopa, ccea e a pay ycooc. aeee yeee oea yce ceae ccey eycoo.

ec ooo opaoe peee aa, a eo, axoee peeoo oea yce. Opeo OM''0 (pc. 6.35) cooecye peeoy ae oea (an)p, aee oopoo oo oca o epoaaoy ooe po Mxaoa opeo M2M0.

Oe e apaepo cce a ee ycooc, oo oyc pepe Haca. B aece pepa e paccopea ccea peeo opa c pe epo e (pc. 6.36), oopo Ayo-aoe xapaepc paoyo cce pax ae oea yce k = K1 K2 K3 opaea a pc. 6.37, a.

Pc. 6.37 AX caeco cce peeo opa:

a pax oeo yce;

epae opax ee e acaa Bce xapaepc oy oye "epoaao" ye ee acaa, pe yoee e epa xapaepcy c o acao, a e aca opa eee e acaa. B o cyae ocaoo epa oy AX pa acea yea paep opea OA, paoo ee, o coo e pa, o coo yeaec oe yce. p o oa A ye epeeac pao (pc. 6.37, ). p ao ae oea yce k cce aca e OA e, oa A axoc ooe A1. B o cyae AX paoyo cce e oxaae oy A1, , ceoaeo, aya ccea ycoa. p yee oea yce k aca e yeaec, peca oa ec apao p k = kp aae ooee A2, ccea axoc a pae ycooc.

p k > kp peca oa pooae epeeac apao, aae ooee A3, ccea caoc eycoo.

Be oea yce a ycooc, coy pep Haca, oo poce cce cooo opa, acoc, c "oopa" xapaepca (pc. 6.38, a). B o cyae p ao ae oea yce peca oa axoc ooe A1, aya ccea ycoa. eee oea yce epeae oy ooee A2, k = kp1, ccea xo a pay ycooc. aeee yeee oea yce po ccey eycooc, a a peca oa aae ooee A3 oxaaec AX.

ooee A4, oopo k = kp2, ec pae ycooc, a ooee Apeco o ycoo, a a e oxaaec AX. Ta opao, oo cea cey o.

Ccea ycoa p ax aex oea yce k < kp1 p ocaoo ox k > kp2, ee e pa ycooc p k = kp1 k = kp2, eycoa p kp1 < k < kp2.

Pc. 6.38 AX cce cooo opa:

a "oopaa" AX epoo opa; "oopaa" AX opoo opa Pc. 6.39 AX pocx cce:

a AX cce epoo opa; AX cce opoo opa Aa ayo-aoo xapaepc paoyo cce, opaeo a pc.

6.38, , oaae, o ccea ee p peex ae oea yce k1p, k2p, k3p, cooecye oa A2, A4, A6 pae ycooc. p aex oea yce k < kp1, kp2 < k < kp3 ccea ycoa (o A1, A5), a p aex kp1 < k < kp2, k > kp3 ccea eycoa (oa A3, A7).

peee pep Haca cceoa oee pocx cce - cce epoo opoo opa oaae, o ec paoya ccea ec cceo epoo opa e aaa, o a ec apaep cce, AX paoyo cce cea ye pacoaac eepo apae (pc. 6.39, a) , ceoaeo, aya ccea cea ye ycoo.

paoyx cce opoo opa AX pacoaaec e oyococ , ceoaeo, a ec ee apaep, AX oa e oxaae oy ( 1, i0), cceyea aya ccea cea ye ycoo.

Tae c oo pepe ycooc Mxaoa Haca oy pee opoc caa cce. B acoc, o cocoo caa ec eee o opaeo c.

6.8.5 Aa ycooc o oapec aco xapaepca B eepo pae oa aa ycooc poo o oapec aco xapaepca, ocpoee oopx poe, e ayo-aoo xapaepc. Ec poce acoc ey oeee AX paoyo cce oapeco ayo-acoo oapeco aoacoo xapaepca, o oo copypoa pep Haca peeo oapec aco xapaepca.

oo, o ccea aoaecoo ypae a ycoo, eoxoo ocaoo, o paoc ey co ooex opaex epexoo oapeco aoaco Pc. 6.40 acoe xapaepc:

a AX; oapece acoe xapaepc o xapaepco px (2j + 1), e j = 0, 1, 2,... o cex oacx, e oapeca ayo-acoa xapaepca ooea, a paa, e m co pax ope xapaepccoo ypae paoyo cce.

Ha pc. 6.40 pee AX paoyo cce cooecye e AX X.

Aa acox xapaepc oaae, o paoc ey co ooex opaex epexoo paa y, o ec aya ccea ye ycoa oo o cyae, ec pae op yy ocycoa, .e. paoya ccea oa ycoo.

6.9 -PAEHE B . 6.7 o paccopeo ocpoee oace ycooc c cooae pep ypa aece pepa ocpoea epoa Bepacoo. Ha pae coyc pye oee oe eo cceoa pax apaepo cce a ee ycooc, .e. papaoa ceye ceae eo ocpoe oace ycooc:

1) ye aaa epeee ope xapaepcecoo ypae ococ ope eo opeoo oopaa;

2) ye aaa ca ope xapaepcecoo ypae, eax pao oyococ, pocpace apaepo cce eo -paa pocpaca apaepo, oop peoe papaoa 1948 . Heapo.

6.9.1 oe -pae Paccop xapaepcecoe ypaee ayo cce n-o opa, oopoe cea oe peeo y:

D(s) = sn + a1 sn-1 +... + an = 0 (a0 = 1). (6.57) peca cee oopaoe pocpaco, oc oopoo c oe ypae, oo oyo aae pocpaco oeo. ao oe oo pocpaca cooecy opee cee ae oeo ypae cooecy oo n- cee, oop ee n ope, acx o cex ae oeo ai. Ec e oe, o op yy epeeac oeco ococ ope oo ypae Paccop ypaee peeo opa D(s) = s3 + a1 s2 + a2 s + a3 = 0 (6.58) cooecyee ey pocpaco oeo a1, a2, a3 (pc. 6.41).

ao oe pocpaca cooecye oe opeee oo oe opeeee p op.

Hapep, oa M ee oopa {a1M, a2M, a3M}, ceoaeo, xapaepcec oo acaec e D(s) = s3 + a1M s2 + a2M s2 + a3M ee op S1M, S2M, S3M.

oa o ope pae 0 +i, oa oa pocpaca ye yoeop ypae D(i ) = (i )3 + a1(i )2 + a2(i ) + a3 = 0.

p < < oy ypae cooecye eoopa oepxoc Q.

Pc. 6.41 C ope xapaepcecoo ypae pocpaca oeo:

a ococ ope xapaepcecoo ypae;

pocpaco apaepo Ec op e, o oa pocpace oeo oaae a y oepxoc Q. p epecee ee op epexo oo oyococ pyy.

Ta opao, oepxoc Q paee ce pocpaco a oac c pa oeco pax ex ope, x ooaa D(m), e m co pax ope xapaepcecoo ypae.

Paee pocpaca apaepo a oac c oao co pax ope yp ao oac eee cpe oyex oace oac ycooc aaec eoo -pae.

ypae peeo opa oo e 4 oac D(3), D(2), D(1), D(0), oce ye oac ycooc.

Ec ec e ce oe, a ac x, apep, a1 a2, p a3 = const, o eco oepxoc oy , oopa ec ceee oepxoc Q paee ococ oeo a1, a2 a oac c oao co pax ope (pc. 6.42).

Pc. 6.42 paa -pae ococ oeo paee pa -pae oya xapaepcecoo ypae cce aeo s = i.

D(i ) = (i )n + a1 (i )n-1 + + an = 0. (6.59) pay -pae oo cpo e oo pocpace oeo epeaoo ypae, o pocpace apaepo cce.

6.9.2 -paee o ooy apaepy yc peyec c e a ycooc aoo-o apaepa v, eo xoeo xapaepcecoe ypaee. o ypaee oo pec y D(s) = M(s) + v N(s) = 0. (6.60) paa -pae opeec a D(i ) = M(i ) + v N(i ) = 0, (6.61) oya v = = X() + i Y(). (6.62) aa ae o o, oo c X() Y() ocpo pay pae, pay cpo oo > 0, a < 0 oya epa oopaee (pc. 6.43).

Ec ococ oecx ope ac o o oc p ee o o pxoa ee cea, o ococ apaepa v oy e ye cooecoa ee o pae -pae, oopy ae pxy cea. Ec e ococ v epecea pay -pae o apae pxo (1) (pc 6.43), o oy cooecye epexo op pao oyococ ey, ec e po pxo o ope epexo eo oyococ pay. Ec pxoa oa, o y oc epecea a op.

opeee oac ycooc ocaoo a pacpeeee ope p ao-o oo ae apaepa v. epexo ococ v o ooo apaepa pyoy, o cy epecee pa -pae, apae cy pxoo oo opee aee D(m).

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