
biryukov samavaakyam

dynamic sistangalekkurichulla padanatthil, paddim biryukov (1946) nte perilulla biryukov samavaakyam (allengil biryukov oosilettar), nananja oosilettarukale maathrkayaakkaan upayogikkunna oru noonn-leanier second oordar deferential samavaakyamaan.
samavaakyam nalkiyirikkunnath 
soothravaakyam _ 1
evideyaanu positteev aaya oru peacewise konsttant function, cheriyath ozhike
soothravaakyam _ 2
iii. kyu. (1) lionard samavaakyathinte oru prathyeka kesaanu; ithu oottoo-oossileshanukale vivarikkunnu.
pariharam (1) oru prathyeka samaya edavelakalil f (y) sthiramaayirikkumbol nalkunnathu
soothravaakyam _ 3
evide exponential functione soochippikkunnu. ivide 
formula _ 4
padaprayogam (2) yadhaarthavum sankeernavumaaya moolyangalkku upayogikkaam.
formula _ 5-leeii aadya pakuthi kaalayalavinte pariharam ithaanu 
soothravaakyam _ 6
randaam pakuthiyude pariharam ithaanu
soothravaakyam _ 7
parihaaratthil samyojanathinte naalu sthiraangangal adangiyirikkunnu, avaykkidayilulla kaalayalavum athirthiyum kandethanam. oru athirthi vyavastha ennathu aantintity yill ninnaan uruthirinjathu.
angane sthiramaaya modil (1) ennathinte pariharam beejaganita samavaakyangalude oru samvidaanam ingane pariharikkunnathiloode labikkum
soothravaakyam _ 8
levenberg-markward algoritam vazhiyaan samyojana sthiraangangal labhikkunnath. 
formula _ 9, formula _ 10 eq. (1) vaan derr pooll oosilettar ennu namakaranam cheythu. athinte pariharam praadhamika pravarthanangalkku adanja roopathil prakadippikkaan kazhiyilla.