Hurwitz nombandela. Ukuzinza sokunquma Wald, Hurwitz Savage

Isihloko iphatha imiqondo ezifana Hurwitz umbandela, Savage futhi Wald. I igxila ngokuyinhloko ngowokuqala. Hurwitz umbandela kuchazwa ngokuningiliziwe kokubili kusuka iphuzu algebraic umbono futhi kusukela iphuzu izinqumo ngaphansi ukungaqiniseki.

Kufanele uqale nge kwencazelo nomqondo nokusimama. It ephawula ikhono kohlelo ukubuyela yakhoibrium ekupheleni ngesiphazamiso, okuyinto esephula ibhalansi ekhona ngaphambili.

Kufanele kuqashelwe ukuthi umphikisi wakhe - uhlelo engazinzile - sisuswa ngokuqhubekayo esimweni ezikuso yakhoibrium (oscillates bazungeza) nge amplitude ukubuyela.

Ukusimama zindlela: definition, izinhlobo

Lokhu iqoqo imithetho asivumela ukuba wahlulele izimpawu ekhona isici kwesibalo ngaphandle kokushesha isinqumo sakhe. Futhi yokugcina, esikhundleni salokho, unikeze ithuba lokuzinqumela nokusimama uhlelo oluthile.

Njengomthetho, zingabantu:

• Algebra (ukulungiselela othile isici kwesibalo algebraic izinkulumo kusetshenziswa imithetho ekhethekile agcwele ukuzinza ACS);
• imvamisa (into cwaningo - imvamisa izici).

Hurwitz ukuzinza umbandela kusukela iphuzu algebraic umbono

Bakhetha i umbandela we-Aljibhra, lokusho kuhlolwe ethile kwesibalo isici ngesimo sefomu ejwayelekile:

A (p) = aᵥpᵛ + aᵥ₋₁pᵛ¯¹ + ... + a₁p + a₀ = 0.

Ngokusebenzisa okuza yayo-matrix kwakhiwa Hurwitz.

Rule sokuhlanganiswa Hurwitz-matrix

Ohlangothini phansi ngokulandelana ebhaliwe kuzo zonke okuza elihambisana ezothando isici kusuka aᵥ₋₁ ukuze A0. Zonke amakholomu ngezansi okuza main idayagonali abonisa degrees elandayo opharetha p, bese phezulu - ngincipha. izinto ezingekho kufakwe amaqanda.

Kukholakala ukuthi uhlelo uzinzile lapho zonke izingane idayagonali kubhekwe-matrix omuhle. Uma determinant main ilingana kuqanda, ukuze kamuva sikhulume mayelana nokuthola yakhe emngceleni ukuzinza, aᵥ = 0. Endabeni kuhambisana nezinye izimo uhlelo okukhulunywa sise umngcele ukuzinza aperiodic entsha (penultimate Minor ilingane no-zero). Lapho izingane omuhle ezisele - kakade umngcele ukuzinza vibrational.

Izinqumo ngaphansi ukungaqiniseki: Wald test, Hurwitz Savage

Ziyakwazi nenqubo yokukhetha efaneleka kakhulu isu ukuhluka. Lokunquma Savage (Hurwitz, Wald) sisetshenziswa esimweni lapho kukhona esingachaziwe imvelo priori kwenzeke uthi. isisekelo wabo - ukuhlaziywa matrix ingozi noma inkokhelo-matrix. Endabeni ukusatshalaliswa esingaziwa uthi ikusasa we kwenzeke lonke ulwazi olutholakala kukhawulwe uhlu ongakhetha yayo.

Ngakho, kufanele uqale nge maximin umbandela Wald. Uyena umbandela ongenathemba kakhulu (ingqapheli ngokucophelela). Lokhu umbandela zingase zimiswe futhi amasu okumsulwa kanye elixutshiwe.

It lethiwa ngokusekelwe ekucabangeleni mayelana okungeziwe ukuthi imvelo ingafinyelela isimo lapho abazuzi akhiwa ukubaluleka aphansi.

Lokhu umbandela nsé engenathemba, esetshenziselwa ngokuhamba ukuxazulula-matrix imidlalo, ngokuvamile ngo amasu okumsulwa. Ngakho, khetha kuqala kusukela umugqa ngamunye inani eliphansi timphawu. Isu isinqumo umenzi, wadedelwa, okuhambelana isici esiphezulu phakathi ubuncane kakade ezikhethiwe.

Ekhethwe umbandela ongakhetha kucatshangelwe ngaphandle ingozi, njengoba umenzi isinqumo yi akukho okubi kakhulu ukwedlula omunye elikhonza benchmark.

Ngakho, efaneleka kakhulu, ngokusho umbandela we Wald, waqaphela isu net, njengasezulwini nasezimweni ezimbi kakhulu, kuqinisekisa aphakeme kunomvuzo onganakiwe.

Ngaphezu kwalokho, kuhle ukucabangela umbandela we Savage. Lapha kukhethwa 1st izixazululo etholakala umkhuba, bathambekele ayeke ngaleso, okuzoba nomphumela nomthelela othize uma kukhethwa zaziyoqhubeka okungalungile.

Ngokwalesi simiso, noma yikuphi isixazululo libhekene eliningi ezithile ukulahlekelwa ezengeziwe ezivela inkambo yalo, uma iqhathaniswa nayo ezekhethelo ngesikhathi isimo nemvelo. Kuyacaca ukuthi isinqumo esifanele akakwazi ungene kukho ukulahlekelwa ezengeziwe, yingakho value abo is nil. Ngakho, njengoba isu ezifanele kakhulu esenziwayo, inani ukulahlekelwa okuyinto incane kanti okubi isethi izimo.

Umbandela ongenathemba-sokulindela okuhle

ezahlukene Ngakho libizwa Hurwitz nenqubomgomo. I izixazululo inqubo Ukukhetha, kokuhlaziywa kwamathenda isimo esikhundleni ezimbili ezeqisayo abanamathela okuthiwa isikhundla Lesisemkhatsini, okuyinto uyakucabangela Amathuba kokubili evumayo nangenkathi okubi kakhulu kwenzeka ukuziphatha imvelo.

Lokhu kwasikiselwa ukuthi ukusilela Hurwitz. Ngokusho kwakhe, nganoma yisiphi isixazululo uzodinga ukufaka inhlanganisela komugqa le imiz kanye max, bese ukhethe isu esifanelana value abo eliphakeme.

Lapho walungisiswa isicelo sale umbandela?

Hurwitz umbandela ukusebenzisa advantageously esimweni libhekene izici ezilandelayo:

1. Kunesidingo ka ikhumbula inketho okubi kakhulu.
2. Ukuntuleka kolwazi mayelana kwenzeke uthi bemvelo.
3. Lokucabanga engatsho lutho.
4. Zilandelwa ngu inombolo ngokwanele elincane izixazululo.

isiphetho

Ekugcineni kuwufanele kokusho ukuthi esihlokweni nenqubo Hurwitz, Savage futhi Wald babebhekwa njengabantu. Hurwitz umbandela wachaza ngokuningiliziwe nge nemibono engafani.