鐭╅樀鍒嗚В鏄寚鏍规嵁涓�瀹氱殑鍘熺悊鐢ㄦ煇绉嶇畻娉曞皢涓�涓煩闃靛垎瑙ｆ垚鑻?/p>
骞蹭釜鐭╅樀鐨勪箻绉�傚父瑙佺殑鐭╅樀鍒嗚В鏈夊彲閫嗘柟闃电殑涓夎锛?/p>
LU
锛夊垎瑙ｃ�佷换
鎰忔弧绉╃煩闃电殑姝ｄ氦涓夎
锛?/p>
QR
锛?/p>
鍒嗚В銆?/p>
瀵圭О姝ｅ畾鐭╅樀鐨?/p>
Cholesky
鍒嗚В锛?/p>
浠ュ強浠绘剰鏂归樀鐨?/p>
Schur
鍒嗚В銆?/p>
Hessenberg
鍒嗚В銆?/p>
EVD
鍒嗚В銆?/p>
SVD
鍒嗚В銆?/p>
GMD
鍒嗚В绛夈�?/p>
(1)
鍙�嗘柟闃电殑
LU
鍒嗚В
鐭╅樀鐨?/p>
LU
鍒嗚В灏辨槸灏嗕竴涓煩闃佃〃绀轰负涓�涓氦鎹笅涓夎鐭╅樀鍜屼竴涓笂
涓夎鐭╅樀鐨勪箻绉舰寮忋�?/p>
绾挎�т唬鏁颁腑宸茬粡璇佹槑锛?/p>
鍙鏂归樀
A
鏄潪濂囧紓鐨?/p>
锛堝嵆鍙�嗙殑锛?/p>
锛?/p>
LU
鍒嗚В鎬绘槸鍙互杩涜鐨勩�?/p>
褰?/p>
L
涓哄崟浣嶄笅涓夎鐭╅樀鑰?/p>
U
涓轰笂涓夎鐭╅樀鏃讹紝
姝や笁瑙掑垎瑙ｇО涓烘潨鍒╃壒
(Doolittle)
鍒嗚В銆傚綋
L
涓轰笅涓夎鐭╅樀鑰?/p>
U
涓哄崟浣嶄笂涓夎鐭╅樀鏃讹紝姝?/p>
涓夎鍒嗚В绉颁负鍏嬪姵鐗?/p>
(Crout)
鍒嗚В銆傛樉鐒讹紝濡傛灉瀛樺湪锛岀煩闃电殑涓夎鍒?/p>
瑙ｄ笉鏄敮涓�鐨勩�?/p>
锛?/p>
PS
锛氭柟闃?/p>
A
鍙敮涓�鍦板垎瑙ｄ负
A=LDU(
鍏朵腑
L
锛?/p>
U
鍒嗗埆涓哄崟浣嶄笅锛屼笂涓?/p>
瑙掔煩闃碉紝
D
涓哄瑙掔煩闃?/p>
)
鐨勫厖鍒嗗繀瑕佹潯浠朵负
A
鐨勫墠
n-1
涓『搴忎富瀛愬紡
閮戒笉涓?/p>
0
銆傜壒鍒細瀵?/p>
n
闃跺绉版瀹氱煩闃碉紝瀛樺湪涓�涓潪濂囧紓涓嬩笁瑙掔煩闃?/p>
L
锛屼娇寰?/p>
A=LL'
鎴愮珛銆?/p>
锛?/p>
MATLAB
鎻愪緵鐨?/p>
lu
鍑芥暟鐢ㄤ簬瀵圭煩闃佃繘琛?/p>
LU
鍒嗚В锛屽叾璋冪敤鏍煎紡涓猴細
[L,U]=lu(X)
锛氫骇鐢熶竴涓笂涓夎闃?/p>
U
鍜屼竴涓彉鎹㈠舰寮忕殑涓嬩笁瑙掗樀
L(
琛?/p>
浜ゆ崲
)
锛屼娇涔嬫弧瓒?/p>
X=LU
銆傛敞鎰忥紝杩欓噷鐨勭煩闃?/p>
X
蹇呴』鏄柟闃点�?/p>
[L,U,P]=lu(X)
锛氫骇鐢熶竴涓笂涓夎闃?/p>
U
鍜屼竴涓笅涓夎闃?/p>
L
浠ュ強涓�涓疆
鎹㈢煩闃?/p>
P
锛屼娇涔嬫弧瓒?/p>
PX=LU
銆傚綋鐒剁煩闃?/p>
X
鍚屾牱蹇呴』鏄柟闃点�?/p>