
ghoornan avanatata takneekon key madhyam seey sanket maapdandon kaa anuman

anuman siddhant mein, ghoornan aparivartaniya takneekon (aspirit) key madhyam seey sanket maapdandon kaa anuman prishthabhoomi shore mein signsoid key mishran key maapdandon koo nirdhaarit karane kii ack takneek haye. iss takneek koo sabse pahale aavritti anuman key liye prastaavit kiya gayaa haye, halanki, dainik upayog praudyogiki mein charanbaddh-sarani pranaliyon kii shuruat key saath, iska upayog aagaman anuman key konn key liye bhee kiya jaataa haye.
samanya vivaran.
aabhaasi upa-sarani mein vibhajit.
ack sanket sadish koo iss prakaar paribhaashit karna,
sootra _ 1
jahan sootra _ 2 sootra _ 3-th signsoid kii radial aavritti kaa pratinidhitva kartaa haye, sootra _ 4 sankhya mein signsoid key liye ack vandermond matricks kaa nirmaan kiya jaa sakata haye, jaisa kii
sootra _ 5
matricks sootra _ 6 koo dou samoohon mein vibhajit kiya jaa sakata haye,
sootra _ 7
aur
sootra _ 8
jahan sootra _ 9 aakar sootra _ 10 kaa ack pehchaan matricks haye. yeh spasht haye kii sootra _ 11 mein sootra _ 6 kaa pahala sootra _ 12 panktiyaan hain, jabaki sootra _ 14 mein sootra _ 6 kii antim sootra _ 12 panktiyaan hain. isase, hamaare paas vaha haye
sootra _ 17
yahaan, sootra _ 18 ack vikarn matricks haye, jahan isake vikarn tatvon koo ack sadish mein likhaa jaa sakata haye.
sootra _ 19
dusare shabdon mein, h key vikarn tatva, sett sootra _ 20 kii radial aavrittiyon key saath jatil ghatank hain. yahaan, yeh spasht haye kii h matricks sootra _ 21 parr ack ghoornan lagu kartaa haye. aspirit maapa gayaa detta key sahprasaran matricks seey samaan ghoornan kaa shoshan kartaa haye.
sanket upa-sthaan anuman.
algorithm koo samajhane key liye, aaie humm r koo maapa gayaa detta key sahprasaran matricks key roop mein niroopit karein. r key eigen value apghatan kii ganana karke (ekvachan moolya apghatan jaise algorithm key madhyam seey), nimnalikhit likhaa jaa sakata haye,
sootra _ 22
jahan e ack vikarn matricks haye jisamen ghatate crum mein r key igen maan hotey hain. yahaan, shore key vicharan seey adhik igenvalue kaa pataa lagaakar, humm orthonormal igenvectors koo yuu seey alag curr sakate hain, joe inn igenvalue key anuroop hain. ise sootra _ 23 key roop mein nott kiya jaa sakata haye jahan hamane kewal pahale k collum rakhe they. 
pahale kii tarah, humm aiss parr nimnalikhit prithakkaran curr sakate hain,
sootra _ 24 aur sootra _ 25.
aparivartaniyata sameekaran kaa samadhan.
isake alawa, s aur sootra _ 26 jaise key beach ack sambandh maujood haye, jahan matricks f kii samagri gyaat haye, lekin vartamaan vishay key liye aprasangik haye. humm nimnalikhit sambandh praapt curr sakate hain,
sootra _ 27
(jahan hamane sootra _ 28 aur sootra _ 29 kaa upayog kiya).
yeh spasht haye kii matricks pee mein aavritti samagri key sambandh mein ghoornan jaankaari hoti haye, jaise kii orthonormal igenvector key pahale sett parr ghoornan dusare sett koo praapt hotaa haye. isake alawa, p key eigen maan h key vikarn tatvon key barabar hain. 
isaliye, pee key liye nimnalikhit sameekaran koo hull karke,
sootra _ 30 
humm aavritti samagri kaa anuman lagaa sakate hain. ise praapt karane key liye, uparokt sameekaran koo chhadm vyutkram (nyuntam vargon key madhyam seey) vidhi seey hull kiya jaa sakata haye.
aisaa karane key liye, sootra _ 31 likhaa jaa sakata haye. 
aavritti kaa anuman.
anta mein, pee key eigen maanon key konon koo dhundhkar, koee bhee nirdhaarit sootra _ 20 kaa anuman lagaa sakata haye.
algorithm kaa udaaharan.
aspirit algorithm key karyanvayan key liye ack chhadm code neeche diyaa gayaa haye.
 falan aspirit ("y", "model _ order", "sankhya _ srot"):
 "m" = model _ order
 "n" = sroton kii sankhya
 shore maap y seey sahprasaran matricks r banaaen. r kaa aakar (m-by-m) hoga.
 aar key aiss. vee. dee. kii ganana karein
 [yuu, ee, vee] = svd (aar)
 sroton key anuroop orthonormal igenvector praapt karein
 "s" = u (:, 1: n) 
 orthonormal igenvector koo dou bhaagon mein vibhajit karein
 s1 = s (1: m-1,:) aur s2 = s (2: m,:)
 pee kii ganana ls (matlab kaa backslash operator) key madhyam seey karein.
 "pee" = aiss1 \aiss2 
 pee key eigen maanon key konon koo khojen
 "doubleu" = konn (ee. aaee. jee. (pee.))/(2 * paaee * alaspacing)
 doa = asind (doubleu)% archesine koo degree mein laker doa konn koo lautaata haye 
 vaapas 'dou' karein"