
konjugettu gradient reethiyude vyulppannam

samkhyaa rekheeya beejaganithathil, rekheeya samvidaanam samkhyaaparamaayi pariharikkunnathinulla oru aavarthana reethiyaanu konjugettu gradient reethi.
ivide soothravaakyam _ 2 ennathu samamiti positteev-dephinit aanu. optimaiseshanulla konjugettu direction reethiyude specialisation, eejan value prasnangalkkulla arnoldi/lanxos ittareshante vyathiyaanam ennivayulppede niravadhi vyathyastha veekshanakonil ninnu konjugettu gradient reethi uruthirinjekkaam.
eee vyulppannam nirmmikkunna pradhana gattangal rekhappeduthuka ennathaanu eee lekhanathinte uddeshyam.
konjugettu dishayil ninnulla vyulppannam.
quadratic function minimise cheiyunnathinu prayogikkunna konjugettu direction reethiyude oru prathyeka kesai konjugettu gradient reethiye kaanaan kazhiyum.
konjugettu dishareeti.
minimise cheiyunnathinulla konjugettu dishayil
oraal oru prarambha ooham formula ninnu aarambikkukayum anubandha avashishta formula ninnu aarambikkukayum formulakal upayogichu aavarthanavum seshiyum kanakkaakkukayum cheiyunnu.
ivide soothravaakyam _ 8 paraspara samyojitha dishakalude oru parambarayaanu, i.iii.,
eathenkilum formula _ 10 nuu.
dishakalude formula thiranjedukkunnathinu soothravaakyangalonnum nalkiyittilla enna ardhathil konjugettu disha reethi krithyamalla. nirddishta choisukal konjugettu gradient reethi, gausiyan elemination ennivayulppede vividha reethikalilekku nayikkunnu.
arnoldi/lanxos aavarthanathil ninnulla vyulppannam.
rekheeya samvidaanangal pariharikkunnathin prayogikkunna arnoldi/lanxos aavarthanathinte oru vakabhedamaayum kanjugett gradient reethiye kaanaan kazhiyum.
general arnoldi reethi.
arnoldi aavarthanathil, oraal oru vekttar formula _ 12 ll aarambikkukayum krilov subspacinte oorthoonoormal adisthaana formula _ 13 kramena nirmmikkukayum cheiyunnu.
soothravaakyam _ 15 nirvachichukondu
mattoru vidhathil paranjaal, formula 17-nuu, formula 20-nuu ethire gram-shmidt oorthooganalaising formula 19 aanu formula 18-neey kandethunnathu.
matricks roopathil vechaal, aavarthanam samavaakyam pidichedukkunnu
evide
koode
leanier sisttangal pariharikkunnathin arnoldi aavarthanam prayogikkumbol, oraal aarambhikkunnath formula _ 6 ll ninnaan, oru prarambha ooham formula _ 5-nuu anuyojyamaaya avashishtam. aavarthanathinte oro ghattathinum sesham, oraal formula _ 26 umm puthiya aavarthana formula _ 27 umm kanakkakkunnu.
nerittulla lanzos reethi.
backie charchakalkku, formula _ 2 samamiti positteev-dephinit aanennu nammal anumaanikkunnu. formula _ 2-nte samamithiyode, mukalile hessenberg matricks formula _ 30 samamithiyayi maarukayum angane trikonamitheeyamaayi maarukayum cheiyunnu. appol athine kooduthal vyakthamaayi soochippikkaan kazhiyum
ithu aavarthanathil formula _ 18-nuu hrasvamaaya moonnu-tame aavarthanathe prapthamaakkunnu, koodaathe arnoldi aavarthanam lanxos aavarthanathilekku churukkunnu.
formula _ 2 samamiti positteev-dephinit aayathinal, formula _ 34 umm. athinaal, formula _ 34 bhaagikamaayi pivot cheyyaathe luu factorise cheyyaan kazhiyum.
formula _ 37, formula _ 38 ennivaykku soukaryapradamaaya aavarthanangalode
formula _ 27 ingane mattiyezhuthuka
koode
athu nireekshikkendathu ippol pradhaanamaan
vaasthavathil, formula _ 44, formula _ 45 ennivaykkum hrasvamaaya aavarthanangalund
eee formulationiloode, formula _ 47-nte lalithamaaya aavarthanathilekku nammal athicherunnu
mukalilulla bandhangal nerittu nerittulla lanzos reethiyilekku nayikkunnu, athu alppam kooduthal sankeernamaanennu maarunnu.
orthogonaalittiyum konjugasy adichelppikkunnathil ninnulla konjugettu gradient reethi.
formula _ 44 skeyil cheyyaanum sthiramaaya gadakathile scalinginu nashtapariharam nalkaanum nammal anuvadikkukayaanenkil, namukk roopathinte lalithamaaya aavarthanangal undakaan saadhyathayunda
lalithavalkaranathinulla parisaramenna nilayil, nammal ippol formula _ 51-nte orthogonaalittiyum formula _ 44, i-yude konjugasi nedunnu.iii., formula _ 10-nuu,
formula _ 51 adisthaanaparamaayi formula _ 56 nte gunithamayathinaal formula _ 57, formula _ 58, formula _ 59,
formula _ 44-nte samyojanam kaanaan, formula _ 62 diagonal aanennu kaanikkan ithu mathiyakum
ithu oresamayam samamitiyum thaazhnna thrikonaakrithiyumaanu, athinaal diagonal aayirikkanam.
51 enna soothravaakyathinte oorthoganaalittiyum 44 enna soothravaakyathinte samyojanavum maathram adichelppichukondu skeyil cheytha formula 44-maayi bandhappett ippol namukk sthiramaaya gadakangalaaya formula 64, formula 65 enniva nedaanaakum.
formula _ 51-nte orthogonaalitti kaaranam, formula _ 70 aavasyamaanu. thalphalamaayi,
athupole, formula _ 44-nte samyojanam kaaranam, formula _ 73 aavasyamaanu. thalphalamaayi,
ithu derivation poortthiyaakkunnu.

