濡備笂琛ㄤ腑锛屽亣瀹氱稉(j墨ng)婵�(j矛)绯荤当(t菕ng)鍖呮嫭n鍊�(g猫)閮ㄩ杸(m茅n)锛屾妸涓婅堪鐢�(ch菐n)鍑虹殑椤�(l猫i)鍒ュ拰鎶曞叆鐨勯(l猫i)鍒ヤ氦鍙夎伅(li谩n)绔嬶紝灏卞舰鎴愭姇鍏ョ敘(ch菐n)鍑鸿〃鐨勫洓鍊�(g猫)璞￠檺銆�

绗厾璞￠檺鏄竴鍊�(g猫)n琛�n 鍒楃殑鐭╅櫍锛屽弽鏄犺波鐗╁拰鏈嶅嫏(w霉)鍦ㄩ儴闁€(m茅n)闁撶殑娴侀噺銆傚湪琛屽垪浜ゅ弶铏�锛屽厓绱�X_ij鍏锋湁闆欓噸鍚京锛屼竴鏂归潰瀹冭〃绀虹暥(d膩ng)鏈熺j閮ㄩ杸(m茅n)鍦ㄧ敓鐢�(ch菐n)閬�(gu貌)绋嬩腑灏�(du矛)绗�i閮ㄩ杸(m茅n)鐢�(ch菐n)鍝佺殑娑堣€楅噺锛屽嵆鍦�j閮ㄩ杸(m茅n)鐢熺敘(ch菐n)閬�(gu貌)绋嬩腑鏈�Xij鏁�(sh霉)閲忕殑i閮ㄩ杸(m茅n)鐢�(ch菐n)鍝佷綔鐐轰腑鍟嗘姇鍏ヨj閮ㄩ杸(m茅n)鎵€娑堣€楋紱鍙︿竴鏂归潰瀹冭〃绀虹暥(d膩ng)鏈�i閮ㄩ杸(m茅n)鐢�(ch菐n)鍝佸垎閰嶇郸j閮ㄩ杸(m茅n)浣跨敤鐨勬暩(sh霉)閲�銆傞€氶亷(gu貌)閫欏€�(g猫)鐭╅櫍锛屽氨灏囧師渚�(l谩i)鎸変笉鍚屾(bi膩o)婧�(zh菙n)鍒嗛(l猫i)鐨勪腑闁撶敘(ch菐n)鍝佸拰涓枔鎶曞叆鏁村悎鍦ㄤ竴璧�銆傜鈪犺薄闄愭槸鏁村€�(g猫)鎶曞叆鐢�(ch菐n)鍑鸿〃鐨勬牳蹇�锛屽厖鍒嗘彮绀轰簡鍦�(gu贸)姘戠稉(j墨ng)婵�(j矛)鍚勯儴闁€(m茅n)涔嬮枔鐩镐簰渚濆瓨銆佺浉浜掑埗绱勭殑鎶€琛�(sh霉)缍�(j墨ng)婵�(j矛)鑱�(li谩n)绯�銆�

绗叀璞￠檺鏄鈪犺薄闄愬湪琛屾柟鍚戜笂鐨勫欢浼�锛�Yi琛ㄧず绗�i閮ㄩ杸(m茅n)鐢�(ch菐n)鍝佺敤浣滄渶绲傜敘(ch菐n)鍝佺殑鏁�(sh霉)閲�銆傛渶绲傜敘(ch菐n)鍝佷竴鑸張鍙垎鐐烘秷璨�(f猫i)銆佽硣鏈舰鎴愬拰鍑哄彛锛屽叾涓墠鍏╅爡(xi脿ng)閭勫彲浠ラ€�(j矛n)涓€姝ョ窗(x矛)鍒�銆傞€欐ǎ绗�II璞￠檺灏辫〃绀哄悇閮ㄩ杸(m茅n)鐢�(ch菐n)鍝佺敤浣滃悇椤�(l猫i)鏈€绲傜敘(ch菐n)鍝佺殑鏁�(sh霉)閲忥紝瀹冧篃鏄竴鍊�(g猫)鐭╅櫍浣嗕竴鑸笉鏄柟闄�銆傛渶绲傜敘(ch菐n)鍝佽垏涓枔鐢�(ch菐n)鍝佺殑鍚堣▓(j矛)鍗崇偤绺界敘(ch菐n)鍝�銆�

绗參璞￠檺鐐虹鈪犺薄闄愬湪鍒楁柟鍚戜笂鐨勫欢浼革紝Vj琛ㄧず绗�j閮ㄩ杸(m茅n)鏈€鍒濇姇鍏�銆傛渶鍒濇姇鍏ヤ竴鑸垎鐐猴細鍥哄畾璩囩敘(ch菐n)鎶樿垔銆佸嫗鍕�(d貌ng)鑰呭牨(b脿o)閰�銆佺敓鐢�(ch菐n)绋呭噲椤嶅拰鐕�(y铆ng)妤�(y猫)鐩堜綑銆傛渶鍒濇姇鍏ヨ垏涓枔鎶曞叆鍚堣▓(j矛)鍗崇偤绺芥姇鍏�銆�

绗叄璞￠檺鍦ㄧ悊璜栦笂鍙嶆槧鏀跺叆鍐嶅垎閰嶇殑鎯呮硜锛屼絾鐢变簬閫欎竴閬�(gu貌)绋嬮洠浠ョ磵鍏ユ渶鍒濇姇鍏ヨ垏鏈€绲傜敘(ch菐n)鍝佹墍妲�(g貌u)鎴愮殑鐭╅櫍妗嗘灦锛屾墍浠ヤ竴鑸偤绌洪爡(xi脿ng)銆�

1锛�  鎶曞叆鐢�(ch菐n)鍑鸿〃鐨勫熀鏈钩琛￠棞(gu膩n)绯�

鍦ㄦ姇鍏ョ敘(ch菐n)鍑鸿〃涓湁涓€浜涘熀鏈殑绺介噺骞宠　闂�(gu膩n)绯�銆傚叿楂旀绱嶅涓嬶細

绺芥姇鍏�=绺界敘(ch菐n)鍑�

涓枔鎶曞叆+澧炲姞鍊�=绺芥姇鍏�

涓枔浣跨敤+鏈€绲備娇鐢�=绺界敘(ch菐n)鍑�

澧炲姞鍊煎悎瑷�(j矛)=鍦�(gu贸)鍏�(n猫i)鐢熺敘(ch菐n)绺藉€�=鏈€绲備娇鐢ㄥ悎瑷�(j矛)

闇€瑕佺壒鍒ユ寚鍑虹殑鏄紝鍦ㄧ附鐢�(ch菐n)鍑鸿垏绺芥姇鍏ヤ箣闁撳叿鏈夊钩琛￠棞(gu膩n)绯�锛屼笉鍍呬竴鍊�(g猫)缍�(j墨ng)婵�(j矛)绺介珨鐨勭附鎶曞叆绛変簬鍏剁附鐢�(ch菐n)鍑猴紝鑰屼笖鍦ㄥ柈鍊�(g猫)閮ㄩ杸(m茅n)灞ゆ涓婄附鎶曞叆涔熺瓑浜庡叾绺界敘(ch菐n)鍑恒€�

 
2锛�  鐩存帴娑堣€楃郴鏁�(sh霉)鑸囧畬鍏ㄦ秷鑰楃郴鏁�(sh霉)鍙婂叾鎳�(y墨ng)鐢�

閫氶亷(gu貌)灏�(du矛)鎶曞叆鐢�(ch菐n)鍑鸿〃閫�(j矛n)琛屾姇鍏ョ敘(ch菐n)鍑哄垎鏋�锛屽彲浠ョ郴绲�(t菕ng)鍙嶆槧鐢�(ch菐n)妤�(y猫)涔嬮枔鐨勯棞(gu膩n)鑱�(li谩n)銆傚叾鍩烘湰鏂规硶鏄互绗厾璞￠檺鐐轰緷鎿�(j霉)锛岄€氶亷(gu貌)涓枔鎶曞叆娴侀噺瑷�(j矛)绠楀悇鐢�(ch菐n)妤�(y猫)闁撶殑鐩存帴娑堣€楃郴鏁�(sh霉)鍜屽畬鍏ㄦ秷鑰楃郴鏁�(sh霉)銆�

鐩存帴娑堣€楃郴鏁�(sh霉)鍙堢ū(ch膿ng)鐐烘姇鍏ョ郴鏁�(sh霉)鎴栨妧琛�(sh霉)绯绘暩(sh霉)锛屼竴鑸敤 琛ㄧず锛屽叾瀹氱京鏄細姣忕敓鐢�(ch菐n)鍠綅j鐢�(ch菐n)鍝侀渶瑕佹秷鑰�i鐢�(ch菐n)鍝佺殑鏁�(sh霉)閲�銆�鐩存帴娑堣€楃郴鏁�(sh霉)鐨勮▓(j矛)绠楀叕寮忔槸锛�

灏�(du矛)鎵€鏈夌敘(ch菐n)妤�(y猫)瑷�(j矛)绠楃洿鎺ユ秷鑰楃郴鏁�(sh霉)锛岀祼(ji茅)鏋滄(g貌u)鎴愪竴鍊�(g猫)绯绘暩(sh霉)鐭╅櫍锛岄€氬父鐢�A琛ㄧず銆傜洿鎺ユ秷鑰楃郴鏁�(sh霉)鍙弽鏄犱簡鐢�(ch菐n)妤�(y猫)闁撶殑鐩存帴鑱�(li谩n)绯�锛屽嵒涓嶈兘鍙嶆槧鐢�(ch菐n)妤�(y猫)闁撹伅(li谩n)绯�銆傞渶瑕佸湪鐩存帴娑堣€楃郴鏁�(sh霉)鍩虹(ch菙)涓婅▓(j矛)绠楀畬鍏ㄦ秷鑰楃郴鏁�(sh霉)锛屾棦鍙嶆槧鐩存帴鑱�(li谩n)绯�锛屼篃鍙嶆槧闁撴帴鑱�(li谩n)绯�銆傚柈鍊�(g猫)瀹屽叏娑堣€楃郴鏁�(sh霉)鐢�b琛ㄧず锛屽皪(du矛)鎵€鏈夌敘(ch菐n)妤�(y猫)瑷�(j矛)绠楀畬鍏ㄦ秷鑰楃郴鏁�(sh霉)锛屾墍褰㈡垚鐨勭煩闄ｇ敤B琛ㄧず锛屽畠鏄緷鎿�(j霉)鐩存帴娑堣€楃煩闄ｈ▓(j矛)绠楀緱鍒扮殑锛屽叾瑷�(j矛)绠楀叕寮忓涓嬶細

B=(I-A)^-1-I

     寮忎腑(I-A)^-1绋�(ch膿ng)鐐哄垪鏄傛儠澶€嗙煩闄�锛屼篃鏄敤渚�(l谩i)鍒嗘瀽鐢�(ch菐n)妤�(y猫)鑱�(li谩n)绯荤殑閲嶈宸ュ叿銆�

濡傛灉鐢�X琛ㄧず绺界敘(ch菐n)鍑哄悜閲�锛岀敤Y琛ㄧず鏈€绲備娇鐢ㄥ悜閲�锛屽墖涓枔浣跨敤鐭╅櫍鐐�AX锛屾牴鎿�(j霉)鎶曞叆鐢�(ch菐n)鍑鸿〃涓殑骞宠　闂�(gu膩n)绯诲彲浠ュ緱鍒帮細

     AX+Y=X

寰炶€屾湁锛�

           (I-A)^-1Y=X

鎶婁笂寮忓(xi臎)鎴愬樊鍒嗗舰寮�锛屽緱鍒�

            (I-A)^-1 銊�Y=銊�X

鍙(ji脿n)鍒楁槀鎯曞か閫嗙煩闄ｅ害閲忎簡鏈€绲備娇鐢ㄨ垏绺界敘(ch菐n)鍑轰箣闁撹伅(li谩n)绯荤殑寮�(qi谩ng)搴�锛屽畠鐨勫惈缇╂槸锛屽鏋滄瘡鍊�(g猫)鐢�(ch菐n)妤�(y猫)鐨勬渶绲備娇鐢ㄩ兘澧炲姞涓€鍊�(g猫)鍠綅锛屽墖鍚勭敘(ch菐n)妤�(y猫)绺界敘(ch菐n)鍑哄皣澧炲姞鐨勫柈浣嶆暩(sh霉)銆�

锛讳緥2-5锛芥牴鎿�(j霉)琛�2-5鎻愪緵鐨勭ず鎰忔€ф暩(sh霉)鎿�(j霉)锛岃▓(j矛)绠楀皪(du矛)鎳�(y墨ng)閮ㄩ杸(m茅n)鐨勭洿鎺ユ秷鑰楃郴鏁�(sh霉)銆�

琛�2-5  鎶曞叆鐢�(ch菐n)鍑�---绀烘剰鏁�(sh霉)鎿�(j霉)

涓婅〃绗厾璞￠檺濡傛灉鐢ㄦ暩(sh霉)瀛�(xu茅)妯″瀷琛ㄧず濡備笅锛氳〃涓殑榛戦珨瀛楁槸瑷�(j矛)绠楃洿鎺ユ秷鑰楃郴鏁�(sh霉)鐨勬暩(sh霉)鎿�(j霉)銆�

鐩存帴娑堣€楃郴鏁�(sh霉)瑷�(j矛)绠楅亷(gu貌)绋嬭綁(zhu菐n)鎻涜〃

		涓枔鐢�(ch菐n)鍑�
		杈�(n贸ng)妤�(y猫)	宸ユキ(y猫)	鍏朵粬	灏忚▓(j矛)
涓� 闁� 鎶� 鍏�	杈�(n贸ng)妤�(y猫) 宸ユキ(y猫) 鍏朵粬	12=X11 17=X21 11=X31	绶ㄨ集鎺ㄨ枽 绲�(t菕ng)瑷�(j矛)甯牨(b脿o)鑰冩浠讹細闁�(k膩i)鍟熶綘鐨勫皥(zhu膩n)妤�(y猫)绲�(t菕ng)瑷�(j矛)涔嬭矾 涓礆(j铆)绲�(t菕ng)瑷�(j矛)甯牨(b脿o)鍚嶆浠跺強鏅�(sh铆)闁� 绲�(t菕ng)瑷�(j矛)甯瓑鏈夊惈閲戦噺鍡�锛熸繁搴﹁В鏋愬姪浣犳槑鏅洪伕鎿� 鍒濈礆(j铆)绲�(t菕ng)瑷�(j矛)甯亷(gu貌)浜嗭紝鏈瑕佸咕骞存墠鑳借€冧腑绱�(j铆)? 鍒嗕韩鍒帮細 绶ㄨ集锛氱挵(hu谩n)鐞冪恫(w菐ng)鏍� 涓婁竴绡囷細2008骞寸当(t菕ng)瑷�(j矛)宸ヤ綔瀵�(sh铆)鍕�(w霉)鍦�(gu贸)姘戠稉(j墨ng)婵�(j矛)寰�(f霉)缈�(x铆)璩囨枡(7) 涓嬩竴绡囷細2008骞寸当(t菕ng)瑷�(j矛)宸ヤ綔瀵�(sh铆)鍕�(w霉)鍦�(gu贸)姘戠稉(j墨ng)婵�(j矛)寰�(f霉)缈�(x铆)璩囨枡(9) 璩囨枡涓嬭級 绮鹃伕瑾茬▼ 鑰佸斧鐩存挱 鐪熼绶寸繏(x铆) 鏇村璩囨枡 鏇村瑾茬▼ 鏇村鐩存挱 缁熻甯�-2021涓骇缁熻瀛﹀熀纭€鐭ヨ瘑鍜岀浉鍏崇煡璇嗙湡棰橈紙绮剧紪鐗堬級 闂呮儳瀹抽敍姝昻 157娴滃搫鍑￠崑姝昻 閸嬫岸顣� 缁熻甯�-2020涓骇缁熻瀛﹀熀纭€鐭ヨ瘑鍜岀浉鍏崇煡璇嗙湡棰橈紙绮剧紪鐗堬級 闂呮儳瀹抽敍姝昻 101娴滃搫鍑￠崑姝昻 閸嬫岸顣� 缁熻甯�-2019涓骇缁熻瀛﹀熀纭€鐭ヨ瘑鍜岀浉鍏崇煡璇嗙湡棰橈紙绮剧紪鐗堬級 闂呮儳瀹抽敍姝昻 152娴滃搫鍑￠崑姝昻 閸嬫岸顣� 鏇村鐪熼 鏈€鏂拌硣瑷� 2025骞村垵涓礆(j铆)绲�(t菕ng)瑷�(j矛)甯煡璀�(sh铆)榛�(di菐n)绮捐瑳锛氱当(t菕ng)瑷�(j矛)瀛�(xu茅)鍩虹(ch菙)鐭ヨ瓨(sh铆)2025-03-27 2025骞村垵绱�(j铆)绲�(t菕ng)瑷�(j矛)甯€冮粸(di菐n)绮捐瑳銆婄当(t菕ng)瑷�(j矛)灏�(zhu膩n)妤�(y猫)鐭ヨ瓨(sh铆)鍜屽(sh铆)鍕�(w霉)銆嬬当(t菕ng)瑷�(j矛)瀵�(sh铆)鍕�(w霉)锛堝惈鐩搁棞(gu膩n)绶寸繏(x铆)椤岋級2025-03-21 2025骞寸当(t菕ng)瑷�(j矛)甯煡璀�(sh铆)榛�(di菐n)鍖附锛氱当(t菕ng)瑷�(j矛)娉曡(gu墨)閮ㄥ垎2025-03-19 2025骞寸当(t菕ng)瑷�(j矛)甯€冭│鐭ヨ瓨(sh铆)榛�(di菐n)绮捐瑳璎涚京锛氱稉(j墨ng)婵�(j矛)瀛�(xu茅)鍩虹(ch菙)鐭ヨ瓨(sh铆)2025-03-14 2025骞寸当(t菕ng)瑷�(j矛)甯€冮粸(di菐n)绮捐瑳锛氭渻(hu矛)瑷�(j矛)鍩虹(ch菙)鐭ヨ瓨(sh铆)2025-03-12 绲�(t菕ng)瑷�(j矛)甯€冭│鏅�(sh铆)闁撳嵆灏囩⒑瀹�锛佺洝鏃╂惗鍏岀当(t菕ng)瑷�(j矛)甯簿鑿绋�锛岄枊(k膩i)鍟�25骞村倷鑰�2025-01-08 绂忓缓鐪佺当(t菕ng)瑷�(j矛)灞€鐧�(f膩)甯�2024骞寸当(t菕ng)瑷�(j矛)甯€冭│鑰冨牬(ch菐ng)瑕�(gu墨)鍓囷細鑰冨墠30鍒嗛悩鎲戞簴(zh菙n)鑰冭瓑鍜岃韩浠借瓑鍏ュ牬(ch菐ng)2024-10-15 鐔鑳屽畬锛�2024骞寸当(t菕ng)瑷�(j矛)甯€冨墠鏁戝懡骞鹃爜(y猫)绱欏尟绺�2024-10-15 鍏嶈不(f猫i)涓嬭級锛�2024骞翠腑绱�(j铆)绲�(t菕ng)瑷�(j矛)甯€冭│-绲�(t菕ng)瑷�(j矛)瀛�(xu茅)鍩虹(ch菙)鐭ヨ瓨(sh铆)-鑰冨墠16闋�(y猫)绱�2024-10-14 鍏嶈不(f猫i)涓嬭級鑰冨墠鐙傝儗12闋�(y猫)绱�锛�2024骞翠腑绱�(j铆)绲�(t菕ng)瑷�(j矛)甯€冭│-绲�(t菕ng)瑷�(j矛)瀵�(sh铆)鍕�(w霉)2024-10-14 鍘诲仛椤� 绲�(t菕ng)瑷�(j矛)甯硣鏍兼煡瑭�(x煤n) 濮ｅ繑妫╂稉鈧紒锟� 濮ｅ繐銇夐幍鎾冲幢缂佸啩绡� 鏉╂稑鍙嗛崑姘额暯 缁旂姾濡紒鍐х瘎 缁旂姾濡惌銉ㄧ槕閻愬湱绮屾稊锟� 鏉╂稑鍙嗛崑姘额暯 閸樺棗鍕鹃惇鐔碱暯 閸樺棗鍕鹃惇鐔碱暯閼板啫澧犲ù瀣槸 鏉╂稑鍙嗛崑姘额暯 濡剝瀚欓懓鍐槸 閸愭彃鍩￠梼鑸殿唽濡剝瀚欑紒鍐х瘎 鏉╂稑鍙嗛崑姘额暯 娑撳洣姹夊Ο陇鈧拷 閼板啫澧犳０妯诲妳鐠侇厾绮� 闁挎瑩顣介張锟� 瀵亶銆嶇划鐐暰缂佸啩绡� 绲�(t菕ng)瑷�(j矛)甯骞寸湡椤屼笅杓� 鏇村 绲�(t菕ng)瑷�(j矛)甯瘡鏃ヤ竴绶� 鎵撳崱鏃ユ 0澶� 绱▓(j矛)鎵撳崱 0浜� 鎵撳崱浜烘暩(sh霉) 鍘绘墦鍗� 闋�(y霉)瑷�(j矛)鐢ㄦ檪(sh铆)3鍒嗛悩 绲�(t菕ng)瑷�(j矛)甯硣鏂欎笅杓� 鏇村 绲�(t菕ng)瑷�(j矛)甯悇鍦板叆鍙� 瀹夊窘 鍖椾含 鍏靛湗(tu谩n) 绂忓缓 寤ｈタ 璨村窞 娴峰崡 娌冲寳 娌冲崡 姹熻槆 閬煎 瀵у 涓婃捣 鍥涘窛 澶╂触 浜戝崡 娴欐睙 鐠�(hu谩n)鐞冪恫(w菐ng)鏍＄Щ鍕�(d貌ng)瑾插爞APP 鐩存挱銆佽伣(t墨ng)瑾层€傝伔閬�(d谩)鏈締(l谩i)锛� 瀹夊崜鐗� 涓嬭級 iPhone鐗� 涓嬭級 閻犲洤澧介埢濂稿椽閵婎煈鍤� 闁哥儐鍠栭幃妤呭嫉瀹ュ懎顫� APP缂佹柨顑呴崳锟�150 婵炲鍔岄崬绱窹P 閻犳劦鍙€椤曞啿饪伴垾鍐叉闁告帞枪閸樸倗鎷硅ぐ鎺濇殭 杩斿洖闋傞儴 鐛插彇椹�(y脿n)璀夌⒓ 绔嬪嵆娉ㄥ唺(c猫) 娉ㄥ唺(c猫)琛ㄧず鍚屾剰銆婄敤鎴�(h霉)鍗�(xi茅)璀般€�鍜�銆婇毐绉佹斂绛栥€� 鍙€�(j矛n)鍏ュ(xu茅)缈�(x铆)涓績鏌ョ湅鏂扮敤鎴�(h霉)娉ㄥ唺(c猫)璐�(z猫ng)绂� 寰俊鎺冪⒓涓€閸电櫥閷� 寰俊鎺冪⒓瀹夊叏鐧婚寗 鍙€�(j矛n)鍏ュ(xu茅)缈�(x铆)涓績鏌ョ湅鏂扮敤鎴�(h霉)娉ㄥ唺(c猫)璐�(z猫ng)绂� 鎺冩弿鍗宠〃绀哄悓鎰�銆婄恫(w菐ng)绔欐敞鍐�(c猫)鍗�(xi茅)璀般€� 出版物经营许可证|京B2-20210770| 京公网安备 11010802033350号|京ICP备16038139号|节目制作经营许可证（京）字20130号 知春路校区：北京市海淀区知春路7号致真大厦D座4层北区（地铁10号线西土城出A口）|邮编：100191 版权所有 2003-2024 北京环球创智软件有限公司|联系客服|营业执照 妫板嫮瀹抽幋鎰 閹劌鍑＄紒蹇斿灇閸旂喖顣╃痪锟� 閼板啳鐦惌顓濅繆閹绘劙鍟� 濞ｈ濮炵€广垺婀囧顔讳繆閸欏嚖绱濋柇鈧幃銊ㄧ箻缂囥倝顣崣鏍ь劅娑旂姾绁弬娆嶁偓浣烘纯閹绢叀顕崇粙瀣搼閿涘矁绻曢懗钘夋嫲閸忔湹绮亸蹇庣串娴肩繝绔寸挧宄邦劅娑旂姳姘﹀ù浣碘偓鍌涘潑閸旂姵妞傜拠宄版礀婢讹拷妫板棗褰�