การแปลงเฮาส, โฮลเดอร, งกฤษ, householder, transformation, ในคณ, ตศาสตร, และในปร, สามม, เป, นการสะท, อนเวกเตอร, บระนาบ, ในปร, คล, เด, ยนท, วไป, เป, นการแปลงเช, งเส, นซ, งเวกเตอร, บระนาบเก, นท, านจ, ดกำเน, ดอ, ลสต, สกอตต, เฮาส, โฮลเดอร, มพ, ผลงานเก, ยวก, บการแปลง. karaeplngehasohledxr xngkvs Householder transformation inkhnitsastr aelainpriphumisammiti epnkarsathxnewketxrkbranab inpriphumiyukhliediynthwip karaeplngehasohledxrepnkaraeplngechingesnsungewketxrkbranabekinthiphancudkaenidxlstn skxtt ehasohledxr tiphimphphlnganekiywkbkaraeplngchnidniepnkhrngaerkinpi ph s 2501 karaeplngehasohledxrepnekhruxngmuxsakhyinkarhakaraeyk QR khxngemthriksniyamaelasmbti aekikhranabekinthicaichsathxnewketxrnnsamarthaethnidodyewketxrhnunghnwy v displaystyle v sungtngchakkbranabekinnntha I displaystyle I khuxemthriksexklksn karaeplngechingesnthiklawinbthnakhxngbthkhwamnisamarthaethnidodyemthriksehasohledxr Q I 2 v v T displaystyle Q I 2vv T odyaemthriksehasohledxrmismbtidngtxipni mnepnemthrikssmmatr Q Q T displaystyle Q Q T mnepnemthriksechingtngchak Q 1 Q T displaystyle Q 1 Q T dngnnmncungepnxawtnakar Q 2 I displaystyle Q 2 I aela Q displaystyle Q sathxnewketxr x displaystyle x id kbranabekinthitngchakkb v displaystyle v odykhxkhwamnisamarthaesdngihehncringidodysmkar Q x x 2 v v T x x 2 v x v displaystyle Qx x 2vv T x x 2 langle v x rangle v emux v x displaystyle langle v x rangle khuxphlkhuncudkhxng x displaystyle x aela v displaystyle v sungmikhaethakbrayahangkhxngcudplaythiimichcudkaenidkhxng x displaystyle x cakranabekinthitngchakkb v displaystyle v dwyehtunicudplaythiimichcudkaenidkhxng Q x displaystyle Qx cungxyukhnlakhangkhxngranabekinkbcudplaykhxng x displaystyle x aelahangcakranabekinethakbrayahangcakcudplaykhxng x displaystyle x kbranabekin klawkhuxepnphaphsathxnkhxng x displaystyle x nnexngkarprayuktichinkaraeyk QR aekikhinkaraeyk QR eratxngkarekhiynemthriks A n n displaystyle A n times n thiakahndihinrup A Q R displaystyle A QR ody Q displaystyle Q epnemthriksechingtngchakaela R displaystyle R epnemthrikssamehliymdanbn erasamarthichkaraeplngehasohledxrinkarkhanwn Q displaystyle Q aela R displaystyle R iddngtxipniih e 1 displaystyle e 1 aethnewketxr 1 0 0 T displaystyle 1 0 dots 0 T thimisunyxyu n displaystyle n tw ih x displaystyle x aethnnxrmkhxngewketxr x displaystyle x id aelaih a 1 displaystyle a 1 epnewketxrhlkthi 1 khxng A displaystyle A aelw kahnd v 1 a 1 a 1 e 1 displaystyle v 1 a 1 a 1 e 1 aela Q 1 I n 2 v 1 v 1 T v 1 2 displaystyle Q 1 I n 2 frac v 1 v 1 T v 1 2 I n displaystyle I n khuxemthriksexklksnkhnad n n displaystyle n times n epnkaraeplngehasohledxrthisathxnewketxrkbranabekinthitngchakkb v 1 displaystyle v 1 aelw eracaidwa Q 1 a 1 a 1 e 1 displaystyle Q 1 a 1 a 1 e 1 hrux Q 1 A a 1 0 A 2 0 displaystyle Q 1 A begin bmatrix a 1 amp star amp dots amp star 0 amp amp amp vdots amp amp A 2 amp 0 amp amp amp end bmatrix odythi A 2 displaystyle A 2 epnemthrikskhnad n 1 n 1 displaystyle n 1 times n 1 klawkhux Q 1 displaystyle Q 1 thaihhlkaerkkhxng A displaystyle A mismachikthiimichsunyxyuephiyngtwediywerasamarthichkrrmwithikhangtnhakaraeplngehasohledxr Q 2 displaystyle Q 2 thithaih Q 1 A 2 0 A 3 0 displaystyle Q 1 A 2 begin bmatrix star amp star amp dots amp star 0 amp amp amp vdots amp amp A 3 amp 0 amp amp amp end bmatrix aela Q 3 displaystyle Q 3 Q 4 displaystyle Q 4 displaystyle dots Q n 1 displaystyle Q n 1 thimiphlechnediywknkb A 3 displaystyle A 3 A 4 displaystyle A 4 displaystyle dots A n 1 displaystyle A n 1 tamladb aelaemuxeraih Q k I k 1 0 0 Q k displaystyle Q k begin bmatrix I k 1 amp 0 0 amp Q k end bmatrix sahrb 2 k n 1 displaystyle 2 leq k leq n 1 aelw eracaidwa Q n 1 Q n 2 Q 2 Q 1 A a 1 0 0 0 0 0 0 0 0 0 0 0 0 R displaystyle Q n 1 Q n 2 cdots Q 2 Q 1 A begin bmatrix a 1 amp star amp star amp dots amp star amp star 0 amp star amp star amp dots amp star amp star 0 amp 0 amp star amp dots amp star amp star vdots amp vdots amp vdots amp ddots amp vdots amp vdots 0 amp 0 amp 0 amp 0 amp star amp star 0 amp 0 amp 0 amp 0 amp 0 amp star end bmatrix R epnemthrikssamehliymdanbn dngnn A Q n 1 Q n 2 Q 1 1 R Q 1 Q 2 Q n 1 R displaystyle A Q n 1 Q n 2 cdots Q 1 1 R Q 1 Q 2 cdots Q n 1 R aelaenuxngcak Q i displaystyle Q i thuktwepnemthrikshasohledxrsungepnemthriksechingtngchak thaih Q Q 1 Q 2 Q n 1 displaystyle Q Q 1 Q 2 cdots Q n 1 epnemthriksechingtngchaktamipdwy A Q R displaystyle A QR cungepnkaraeyk QR tamthieratxngkarkhntxnwithitamthiidbrryaykhangtn samarthnaipekhiynepnopraekrmkhxmphiwetxrthithakarkhanwndwycanwncudeluxnsungmiesthiyrphaphthangtwelkh epnphliherasamarthaeksmkarechingesn aelahakhaechphaaecaacngkhxngemthriksidodykhathihaidcaimkhladekhluxnmaknkhakemthriksthiepnkhxmulekhamielkhenguxnikhtaxangxing aekikhAlston S Householder Unitary Triangularization of a Nonsymmetric Matrix Journal ACM 5 4 1958 339 342 DOI 10 1145 320941 320947 David D Morrison Remarks on the Unitary Triangularization of a Nonsymmetric Matrix Journal ACM 7 2 1960 185 186 DOI 10 1145 321021 321030 bthkhwamekiywkbkhnitsastrniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy khnitsastrekhathungcak https th wikipedia org w index php title karaeplngehasohledxr amp oldid 4702430, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,