Hurwitz rarrabẽwa. Stability Sharudda Wald, Hurwitz Savage

A labarin da hulda da Concepts kamar Hurwitz rarrabẽwa, Savage da Wald. A mayar da hankali ne musamman a kan ta farko. Hurwitz rarrabẽwa aka bayyana a cikin daki-daki, duka daga cikin algebraic ra'ayi da kuma daga batu na yanke shawara a karkashin rashin tabbas.

Ya kamata a fara da definition of manufar dorewa. Yana characterizes da ikon da tsarin komawa zuwa cikakken hankalinsa da karshen rikicin, wanda keta data kasance balance baya.

Ya kamata a lura da cewa abokin hamayyarsa - m tsarin - an cire ci gaba daga ta ma'auni jihar (oscillates a kusa da shi) tare da dawo mawadãta.

Dorewa sharudda: definition, iri

Wannan ya kafa dokoki da damar mu mu yi hukunci da data kasance ãyõyi halayyar lissafi ba tare da neman ya yanke shawara. Kuma karshen, bi da bi, samar da wata damar yin hukunci da dorewa da wani tsarin.

Matsayin mai mulkin, su ne:

• Algebraic (shiri na musamman halayyar lissafi algebraic maganganu amfani da musamman dokokin da faye hali da zaman lafiyar na ACS).
• mita (abu na binciken - mita halaye).

Hurwitz kwanciyar hankali rarrabẽwa daga algebraic ra'ayi

Sun yarda da wani algebraic rarrabẽwa, yana ambaton da shawara na musamman halayyar lissafi a cikin nau'i na misali form:

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

Ta hanyar da coefficients matrix kafa Hurwitz.

Rule tari Hurwitz matrix

A downward shugabanci a cikin tsari da aka rubuta fitar da duk coefficients m ga halayyar lissafi daga aᵥ₋₁ zuwa a0. All ginshikan kasa da babban diagonal coefficients nuna kara digiri na afareta p, sa'an nan up - ragewa. M abubuwa suna maye gurbinsu da zeros.

An yi imani da cewa tsarin ne barga a lokacin da duk diagonal minors dauke m matrix. Idan babban determinant ne ya daidaita da sifili, sa'an nan ba za mu iya magana game da gano ta a kan kwanciyar hankali iyaka, kuma aᵥ = 0. A cikin hali na yarda da sauran yanayi da tsarin a tambaya an located a iyaka da sabon aperiodic kwanciyar hankali (penultimate Ƙananan daidaita da sifili). Lokacin da kyau sauran minors - riga a iyaka da vibrational kwanciyar hankali.

Shawarwari a karkashin rashin tabbas: Wald gwajin, Hurwitz Savage

Su ne ma'auninta na gwada zabi mafi dace dabarun bambancin. Criterion Savage (Hurwitz, Wald) ne amfani a halin da ake ciki inda akwai maras bayyani yanayi priori yiwuwa na jihohi. Su akai - da bincike na cikin hadarin matrix ko nufin samun riba matrix. A cikin hali na unknown rarraba gaba jihohin da yiwuwa duk samuwa bayanai yana da iyaka zuwa cikin jerin ta zaɓuɓɓuka.

Saboda haka, ya kamata mu fara da maximin rarrabẽwa Wald. Shi ne mai rarrabẽwa matsananci mummunan zato (m Kiyayewa). Wannan qa'idar za a iya kafa da kuma tsarki da kuma gauraye dabarun.

Yana samu da sunan dangane da zaton game da extras cewa halitta iya gane jihar da samun darajar daidaita zuwa ga mafi ƙasƙanci darajar.

Wannan qa'idar ne m ga pessimistic, wanda aka yi amfani a cikin shakka daga warware matrix wasanni, sau da yawa a cikin m dabarun. Saboda haka, da farko zaɓi daga kowane layi da m darajar da rabi. dabarun yanke shawara mai yi sai saki, wanda yayi dace da matsakaicin kashi daga cikin riga zaba m.

Zaba ta hanyar da littattafai dauke zabin ba tare da hadarin, kamar yadda hukuncin mai yi fuskantar wani m sakamakon fiye da daya cewa hidima a nasa tarihin.

Saboda haka, mafi dace, bisa ga rarrabẽwa na Wald, gane net dabarun, kamar yadda yake a cikin mafi munin yanayi, tabbatar da mafi m nufin samun riba.

Bugu da ari, yana da daraja idan akai la'akari da qa'idar na Savage. Ga zabi na 1st na samuwa mafita a yi, ayan tsaya a cewa, wanda zai haifar da kadan tasiri idan zabi zai kasance har yanzu ba daidai ba.

Bisa wannan ka'ida, da wani bayani ne halin da wasu yawa na ƙarin asarar tasowa a cikin shakka daga gare ta, a kwatanta da mafi kyau samuwa a jihar yanayi. A fili yake cewa da hakkin yanke shawara ba zai iya haifar da ƙarin hasarori, wanda shi ne dalilin da ya sa da darajar kome ba ne. Saboda haka, kamar yadda mafi dace dabarun da aka soma, da adadin asarar wanda shi ne kadan a mafi mũnin kafa na yanayi.

Da littattafai na mummunan zato-fata

Saboda haka daban-daban da aka kira Hurwitz rarrabẽwa. A selection tsari mafita, da kimantawa da halin da ake ciki maimakon biyu da tsakaitãwa bi zuwa abin da ake kira tsaka-tsaki matsayi, wanda daukan la'akari da yiwuwar duka biyu m da kuma mafi munin yanayin halayyar yanayi.

Wannan na nuna cewa, an cimma Hurwitz. A cewar shi, ga wani bayani zai bukatar ka shigar a mikakke hade da min da max, sa'an nan zabi wani dabarun da ya yi daidai da mafi darajar.

Lokacin da barata bisa ga aikace-aikace na wannan rarrab?

Hurwitz rarrabẽwa a yi amfani da advantageously a halin da ake ciki halin da wadannan siffofin:

1. Akwai bukatar shan la'akari da munin zaɓi.
2. Rashin ilimi game da yiwuwa na jihohin yanayi.
3. Zaton wasu hadarin.
4. Aiwatar da isasshe kananan yawan mafita.

ƙarshe

A karshe shi ne a fadi cewa a cikin labarin an dauke sharudda Hurwitz, Savage da Wald. Hurwitz rarrabẽwa aka bayyana a cikin daki-daki tare da daban-daban da ra'ayoyi.