valalelya hessian vakraresha

ganitat, valalela hessian vakr hessian vakranche samanyikaran darshavito; heey lambvartulakar vakralekhanamadhye jode aanee duheri sutranna gatee denyasathi aanee majbootpane eksandh ankganit thevanyasathi sadar kele gele hote. kahee karyanmadhye (shevatche vibhag pahaa), tyacha veg aadvya vakrareshechya jawal asato.
vyakhya.
keey" heey eka kshetra asoo dya. valalelya hessian vakrannusar bernstein, lang yanni,
aanee cohell.
affine nirdeshank" madheel valavalele hessian swaroop khalilpramane dile aaheh
sootra _ 1
aanee 'prakshepak nirdeshank' madhyeh
sootra _ 2
jethe sootra _ 3 aanee sootra _ 4 aanee "aaa", "keey" madhye "dii"
lakshat ghya qee heey vakr hessian vakranchya dwaiparamparagat samatulya aahet.
hessian vakr heey fakt a = 1 saha valalelya hessian vakrateche eka vishesh prakaran aahe.
a"· "x" 3 + "y" 3 + 1 = "d"· "x"· "y" heey samikaran vicharat ghetalyas, lakshat ghyah
jarr "a" chey "k" madhye ghanmul asel, tarr eka adviteey "b" astitvat aahe, jase qee "a" = "b" 3.otherwise, tarr "k" (e.) chey vistar kshetra vicharat ghene aavashyak aahe.jee., "keey" ("aaa" 1/3)). mug, 'b' 3· 'x' 3 = 'bx' 3, 't' = 'b'· 'x' paribhashit karat asalyane, parivartan karnyasathi khaleel samikaran (heshiyan swarupat) aavashyak aaheh
sootra _ 5.
yacha arth assa qee valalelya heshiyan vakr heey warestrass swarupat lambvartulakar vakrareshechya dwaiparamparagat samatulya aahet.
gut kayada.
lambvartulakar vakrareshechya gut niyamache vishleshan karane, jode aanee duheri sutranchi vyakhya karane manoranjak aahe (kaaran sadhe shakti vishleshan aanee vibhedak shakti vishleshan halle yaa karyanchya chaloo velevar aadharit aahet). sarvasadharanpane, gut kayada khaleel prakare paribhashit keela jaatoh jarr teen bindu ekach reshet asateel tarr tyanchi berries shunyaparyant asate. tarr, yaa gunadharmannusar, gut niyamachi spasht sutre vakr aakaravar avalambun asatat.
samaja "p" = ("x" 1 ", y" 1) haah eka bindu asel, tarr tyacha vyutkram pratalamadhye − "p" = ("x" 1/"y" 1,1/"y" 1) aahe.
prakshepak nirdeshankat, 'p' = ('x': 'y': 'z') haah eka bindu asoo dya, tarr − 'p' = ('x' 1/'y' 1:1/'y' 1: 'z') haah p chaa vyutkram aahe.
yavyatirikt, tatasth ghatak (sanlagn pratalamadhye) aaheh θ = (0, −1) aanee prakshepak nirdeshankatah θ = (0: −1:1).
lambvartulakar vakralekhan aanee purnank gunank (eae. see. emm.) chya lambvartulakar vakr paddhatichya kahee anuprayoganmadhye, kahee purnank "aine" sathee "pii" chya scalar gunakaranchi ganana karane aavashyak aahe, samaja "[aine] pii", aanee teey duheri aanee jode paddhativar aadharit aahet; mhanoon jodani aanee duheri sutranchi aavashyakta aahe.
yaa lambvartulakar vakrareshesathi jode aanee duherikaran sutre paribhashit kelee jaau shakatat, sanketan sope karnyasathi sanlagn nirdeshank vaparunah
atirikt sutre.
samaja "p" = ("x" 1 ", y" 1) aanee "q" = ("x" 2 ", y" 2); mug, "r" = "p" + "q" = ("x" 3 ", y" 3) khaleel samikaranandware dile jaateh
sootra _ 6
sootra _ 7
duheri sutre.
samaja "p" = ("x", "y"); mug [2] "p" = ("x" 1 ", y" 1) khaleel samikaranandware dile jaateh
sootra _ 8
sootra _ 9
algoridam aanee udaharane.
yethe jode aanee duherikaranachya kayadyache kahee karyaksham algoridam dile aahet; teey cryptographic gananet mahatvache asoo shakatat aanee yaa uddeshasathi prakshepak nirdeshank vaparale jaatat.
joda.
sootra _ 10
sootra _ 11
sootra _ 12
sootra _ 13
sootra _ 14
sootra _ 15
sootra _ 16
sootra _ 17
sootra _ 18
yaa algoridamchi kimmat 12 gunakar, eka gunakar a (sthirank) aanee 3 jodani aahe.
udaharaneh
p' 1 = (1: −1:1) aanee 'p' 2 = (− 2:1:1) heey valalelya hessian vakrareshevaril bindu asoo dya, a = 2 aanee d =-2.then 'r' = 'p' 1 + 'p' 2 asey dile aaheh
sootra _ 19
mhanje, "r" = (0: −3: −3).
duppat.
sootra _ 23
sootra _ 24
sootra _ 25
sootra _ 26
sootra _ 27
sootra _ 28
sootra _ 29
yaa algoridamchi kimmat 3 gunakar, eka gunakar sthirank, 3 jodani aanee 3 ghan shakti aahe.
yaa vakrareshesathi midavalela haah sarvottam parinam aahe.
udaharaneh
varr dilelya pramane, 'p' = (1: −1:1) haah a = 2 aanee d =-2 neey paribhashit kelelya vakrareshevaril bindu asoo dya, tarr 'r' = [2] 'p' = ('x' 3: 'y' 3: 'z' 3) hyadvare deela jaatoh
sootra _ 30
mhanje "r" = (−2: −3:5).

