
berkhoff algoridam

berkhoffcha algoridam (jyala berkhoff-vonn-neumen algoridam dekhil mhanatat) haah biostocastic matrixla kramparivartan matrixchya bahirmukh sanyogat vighatit karnyasathicha eka algoridam aahe. 1946 madhye garrett berkhoff yanni too prakashit keela. tyache anek upayog aahet. asach eka arj mhanje yogya yadruchchik assignmentchya samasyesathih vastunche yadruchchik vatap dilyas, berkhoffcha algoridam nirdharit vatpavar lotterymadhye vighatit karoo shakato.
shabdavali.
bistocastic matricks' (jyala 'double-stockestic' asehi mhanatat) haah eka matricks aahe jyamadhye serve ghatak 0 peksha mothe kinwa samaan asatat aanee pratyek pankti aanee stambhatil ghatakanchi berries 1 asate. eka udaharan khaleel 3-buy-3 matricks aaheh
sootra _ 1
kramparivartan matricks" heey dvistariy matrixche eka vishesh prakaran aahe, jyamadhye pratyek ghatak ektar 0 kinwa 1 asato (mhanoon pratyek pankti aanee pratyek stambhat agadi eka "1" asato). eka udaharan khaleel 3-buy-3 matricks aaheh
sootra _ 2
biostocastic matrixche berkhoff vighatan (jyala berkhoff-vonn-neuman vighatan dekhil mhanatat) heey nakaratmak nasalelya vajanansah kramparivartan matrixchi berries mhanoon tyache sadarikaran aahe. udaharanarth, vareel matricks khaleel berries mhanoon sadar keela jaau shakatoh
sootra _ 3
berkhoffcha algoridam input mhanoon biostocastic matricks prapt karato aanee output mhanoon berkhoff vighatan mhanoon parat yeto.
sadhane.
aine"-buy-"aine" matricks "ex" chaa kramparivartan sanch haah "ex" chya "aine" nondincha sanch aahe jyamadhye pratyek panktitoon aanee pratyek stambhatoon achook eka nond asate. danes kanigache eka pramey asey mhanate keeh "pratyek bistocastic matrixcha kramparivartan-sanch asato jyamadhye serve nondi sakaratmak asatat."" "aine" "-buy-aine" "matricks" "ex" "chaa sakaratmak aalekh haah 2" "aine" "shirobindu asalela dvidaleey aalekh aahe, jyamadhye eka bajuche shirobindu" "aine" "pankti aahet aanee dusya bajuche shirobindu" "aine" "stambh aahet aanee tyaa pankti aanee stambhavaril pravesh sakaratmak asalyas eka pankti aanee stambh darmyan eka dhaar aahe". sakaratmak nondinsah kramparivartan sanch haah sakaratmak aalekhatil paripoorn julanichya samatulya aahe. bahupadi velet, udaa. dvidaleey aalekhatil eka paripoorn julani aadhalu shakate.jee. jastit jaast cardinality julanisathi konatehi algoridam vaparane. kanigache pramey khalilpramane aaheh "konatyahi bistocastic matrixcha sakaratmak aalekh eka paripoorn julani swikarato."jarr serve ghatak kamkuvat-sakaratmak asateel aanee pratyek pankti aanee stambhachi berries" see "chya barobarichi asel, tarr matrixla scale-bistocastic mhanatat, jethe" see "haah kahee sakaratmak sthirank aahe. dusya shabdant, heey 'see' gunile bistocastic matricks aahe. sakaratmakatechya aalekhavar scalingcha parinam hott naslyamuleh "konatyahi scale-bistocastic matrixcha sakaratmakatecha aalekh eka paripoorn julani swikarato."
algoridam.
berkhoffcha algoridam haah eka lobhi algoridamah too lobhane paripoorn julani shodhato aanee tyanna apoorn julanitun kadhoon takto. teey khalilpramane karya karate.
algoridam barobar aahe kaaran, payari 6 nantar, pratyek panktitil aanee pratyek stambhatil berries "zed" ["aay"] neey qamee hote. tyamule, matricks "x" scale-bistocastic rahate. mhanoon, tisya tappyat, eka paripoorn julani nehmich astitvat asate.
dhavanyachi vel jatilata.
chauthya tappyat 'zed' ['aay'] nivadidvare, pratyek punaravruttimadhye 'ex' chaa kiman eka ghatak 0 hoto. mhanoon, algoridam jastit jaast 'aine' 2 payyannantar sampane aavashyak aahe. tathapi, shevatchya payarimadhye ekach velee "n" ghatak 0 karane aavashyak aahe, tyamule algoridam jastit jaast "n" 2 − "n" + 1 payyannantar sampato, jeey sootra _ 4 soochit karate.
1960 madhye, jotionson, dulmays aanee mendelsohan yanni dakhavun dile qee berkhoffcha algoridam pratyakshat jastit jaast "n" 2 − 2 "n" + 2 payyannantar sampato, joou sarvasadharanpane ghatt asato (mhanje, kahee prakarananmadhye "n" 2 − 2 "n" + 2 kramparivartan matricks aavashyak asoo shakatat).
nyayya vibhaganimadhye arj.
phair yadruchchik assignment samasyemadhye, 'aine' vastoo aanee 'aine' lock asatat jyanna vastunpeksha bhinn pradhanye asatat. pratyek vyaktila eka vastoo dene aavashyak aahe. nyayyata prapt karnyasathi, vatap yadruchchik kele jaateh pratyek (vyakti, vastoo) jodisathi, sambhavyatechi ganana kelee jaate, jenekarun pratyek vyaktisathi aanee pratyek vastusathi sambhavyatechi berries 1 aahe. sambhavya-malika prakriya sambhavyatechi ganana asha prakare karoo shakate qee pratyek agent, sambhavyatecha matricks pahoon, itar serve lokanchya ranganpeksha tyachya sambhavyatechya rangela pradhanya deto (yaa malmattela matsar-swatantrya mhanatat). yamule haah yadruchchik vatap vyavharat kase amalat aanayache haah prashna upasthit hoto. pratyek vastusathi keval yadruchchikpane vegale karata yet nahee, kaaran yamule vatap houu shakate jyamadhye kahee lokanna anek vastoo midatat tarr itaranna vastoo milat naheet.
yethe, berkhoffcha algoridam upayukt aahe. sambhavyatecha matricks, sambhavya-malika algoridamdware ganana kelee jaate, tee dvistariy aahe. berkhoffcha algoridam tyala kramparivartan matrixchya bahirmukh sanyogat vighatit karoo shakato. pratyek kramparivartan matricks eka nirdharak assignment darshavito, jyamadhye pratyek agentla achookpane eka object midato. asha pratyek matrixcha gunank sambhavyata mhanoon arth lavala jaato; mojalelya sambhavyatevar aadharit, yadruchchikpane eka assignment nivadane aanee tyachi amalbajavani karane shakya aahe.
vistar.
kiman sankhyechya sandnyansah berkhoff vighatan ganana karanyachi samasya aine. pii.-haard asalyache darshavile gele aahe, parantu tyachi ganana karnyasathi kahee shodhanibandh dnyat aahet. heey pramey samanya yadruchchik matrixsathi nirdharak sankraman matricks vistarit kele jaau shakate.
budish, chey, kojima aanee milgram heey vyavharya assignmentvar kahee nirbandhansah, berkhoffchya algoridamche gair-chauras matrixmadhye samanyikaran karatat. teey eka vighatan algoridam dekhil sadar karatat jeey apekshit mulyanmadhil farak qamee karate.
vajirani birkhoffchya algoridamche dvi-pakshiy nasalelya aalekhanmadhye samanyikaran karate.