姝ｅ畾鐭╅樀鐨勬�ц川鍙婂簲鐢?/p>
鎽樿锛?/p>
姝ｅ畾鐭╅樀鏄嚎鎬т唬鏁颁腑涓�涓瀬鍏堕噸瑕佺殑搴旂敤骞挎硾鐨勬蹇碉紝
娣卞叆鎺㈣鍏?/p>
鍩烘湰鎬ц川瀵逛簬鍏朵粬绉戠爺棰嗗煙鐨勭爺绌舵湁鐫�閲嶈鐨勬剰涔夈�?/p>
鍩轰簬姝わ紝
鏈枃棣栧厛瀵规瀹氱煩
闃电殑瀹氫箟杩涜浜嗘弿杩帮紝
鍏舵鐮旂┒浜嗘瀹氱煩闃电殑鎬ц川涓庡垽瀹氭柟娉曪紝
鏈�鍚庣畝鍗曚粙缁嶄簡
鍏跺叿浣撳簲鐢ㄣ�?/p>
鍏抽敭璇嶏細姝ｅ畾鐭╅樀锛涘熀鏈�ц川锛涙帹璁猴紱鍒ゅ畾锛涘簲鐢?/p>
鍓嶈█锛?/p>
鐭╅樀鏄嚎鎬т唬鏁颁腑涓�涓瀬鍏堕噸瑕佺殑搴旂敤骞挎硾鐨勬蹇碉紝
濡傜嚎鎬ф柟绋嬬粍鐨?/p>
涓�浜涢噸瑕佹�ц川鍙嶆槧鍦ㄥ畠鐨勭郴鏁扮煩闃靛拰澧炲箍鐭╅樀鐨勬�ц川涓婏紝
骞朵笖瑙ｆ柟绋嬬粍鐨勮繃绋嬩篃
琛ㄧ幇涓哄彉鎹㈣繖浜涚煩闃电殑杩囩▼锛?/p>
浜屾鍨嬬殑姝ｅ畾鎬т笌瀹冪殑鐭╅樀鐨勬瀹氭�х浉瀵瑰簲锛?/p>
鐢氳嚦
鏈変簺鎬ц川瀹屽叏涓嶅悓鐨勮〃闈笂瀹屽叏娌℃湁鑱旂郴鐨勯棶棰橈紝褰掔粨鎴愮煩闃甸棶棰樺悗鍗存槸鐩稿悓
鐨勩�?/p>
杩欏氨浣跨煩闃垫垚涓轰唬鏁扮壒鍒槸绾挎�т唬鏁扮殑涓�涓富瑕佺爺绌跺璞°�?/p>
浣滀负鐭╅樀鐨勪竴绉?/p>
鐗规畩绫诲瀷锛?/p>
姝ｅ畾鐭╅樀鏈夊緢澶氱壒娈婃�ц川锛?/p>
鏄爺绌朵簩娆″瀷锛?/p>
绾挎�х┖闂村拰绾挎�у彉鎹㈤棶棰?/p>
鐨勬湁鍒╁伐鍏枫�傛湰鏂囧氨姝ゆ祬璋堜竴涓嬫瀹氱煩闃电殑鍚勭鎬ц川鍜屽簲鐢ㄣ�?/p>
1.
姝ｅ畾鐭╅樀鐨勫熀鏈�ц川
1.1
姝ｅ畾鐭╅樀鐨勫畾涔?/p>
璁?/p>
M
鏄?/p>
n
闃跺疄绯绘暟瀵圭О鐭╅樀锛?/p>
濡傛灉瀵逛换浣曢潪闆跺悜閲?/p>
X=(x1
锛?/p>
鈥︹�?/p>
锛?/p>
xn)
閮芥湁
X鈥睲X
锛?/p>
0
锛?/p>
灏辩О
M
姝ｅ畾
(Positive Definite)
銆?/p>
姝ｅ畾鐭╅樀鍦ㄧ浉鍚堝彉鎹笅鍙寲涓烘爣鍑嗗瀷锛?/p>
鍗冲崟浣嶇煩闃点�傛墍鏈夌壒寰佸�煎ぇ浜庨浂鐨勫绉扮煩闃碉紙鎴栧巹绫崇煩闃碉級涔熸槸姝ｅ畾鐭╅樀銆?/p>
鍙︿竴绉嶅畾涔夛細
涓�绉嶅疄瀵圭О鐭╅樀锛?/p>
姝ｅ畾浜屾鍨?/p>
f(x1,x2,鈥?xn)=X鈥睞X
鐨勭煩闃?/p>
A(A鈥?
绉颁负姝ｅ畾鐭╅樀銆?/p>
1.2
姝ｅ畾鐭╅樀鐨勬�ц川
褰撶煩闃?/p>
A
涓烘瀹氱煩闃电殑鏃跺�欙紝鍒欏繀鏈変互涓嬪嚑涓�ц川锛屽嵆锛?/p>
锛?/p>
1
锛?/p>
aii
锛?/p>
0
锛?/p>
i=1
锛?/p>
2
锛?/p>
鈥︹�?/p>
锛?/p>
n
锛?/p>
锛?/p>
2
锛?/p>
A
鐨勫厓绱犵殑缁濆鍊兼渶澶ц�咃紝蹇呭畾涓轰富瀵硅鍏冿紱
锛?/p>
3
锛?/p>
鈮nnAn
-1
锛屽叾涓紝
An-1
鏄?/p>
A
鐨?/p>
n-1
闃朵富瀛愬紡锛?/p>
锛?/p>
4
锛?/p>
鈮11a22鈥︹�nn
锛屽綋涓斾粎褰?/p>
A
涓哄瑙掗樀鐨勬椂鍊欐垚绔嬶紱
鑰岄櫎浜嗕互涓婅繖鍑犱釜鎬ц川澶栵紝
杩樻湁鑻ュ共涓帹璁轰篃鏄瘮杈冮噸瑕佺殑锛?/p>
鍦ㄥ緢澶氬簲鐢ㄤ腑