锘??xml version="1.0" encoding="utf-8" standalone="yes"?>欧美高清在线一区二区,亚洲精品中文字,欧美丝袜一区二区http://m.shnenglu.com/ningfangli-blog/category/3104.html鍔姏銆佸姫鍔涖佸啀鍔姏錛? 娌℃湁浠涔堣兘闃繪鎴戝鐭ヨ瘑鐨勬復鏈涖?/description>zh-cnTue, 20 May 2008 09:49:45 GMTTue, 20 May 2008 09:49:45 GMT60Dijkstra綆楁硶http://m.shnenglu.com/ningfangli-blog/articles/15606.htmlningfangliningfangliThu, 23 Nov 2006 17:13:00 GMThttp://m.shnenglu.com/ningfangli-blog/articles/15606.htmlhttp://m.shnenglu.com/ningfangli-blog/comments/15606.htmlhttp://m.shnenglu.com/ningfangli-blog/articles/15606.html#Feedback2http://m.shnenglu.com/ningfangli-blog/comments/commentRss/15606.htmlhttp://m.shnenglu.com/ningfangli-blog/services/trackbacks/15606.html 浠婂ぉ鏅氫笂瀛︿範浜嗚繖涓畻娉曪紝鐪嬩簡緗戜笂鐨勫ソ浜涜祫鏂欙紝鐢ㄨ嚜宸辯殑鐞嗚В璁板綍涓嬫潵銆?/strong>

Dijkstra綆楁硶鏄敱鑽峰叞璁$畻鏈虹瀛﹀鑹懼吂鏍悸瘋開縐戞柉褰誨彂鐜扮殑銆傜畻娉曡В鍐崇殑鏄湁鍚戝浘鎴栨棤鍚戝浘涓渶鐭礬寰勯棶棰樸?br />綆楁硶鎻忚堪錛?br />聽聽聽聽聽聽聽聽聽榪欎釜綆楁硶鏄氳繃涓烘瘡涓《鐐?i>v淇濈暀鐩墠涓烘鎵鎵懼埌鐨勪粠s鍒皏鐨勬渶鐭礬寰勬潵宸ヤ綔鐨勩傚垵濮嬫椂錛屾簮鐐箂鐨勮礬寰勯暱搴﹀艱璧嬩負0錛?i>d[s]=0錛夛紝 鍚屾椂鎶婃墍鏈夊叾浠栭《鐐圭殑璺緞闀垮害璁句負鏃犵┓澶э紝鍗寵〃紺烘垜浠笉鐭ラ亾浠諱綍閫氬悜榪欎簺欏剁偣鐨勮礬寰勶紙瀵逛簬V涓墍鏈夐《鐐?i>v闄?i>s澶?i>d[v]= 鈭烇級銆傚綋綆楁硶緇撴潫鏃訛紝d[v]涓偍瀛樼殑渚挎槸浠?i>s鍒?i>v鐨勬渶鐭礬寰勶紝鎴栬呭鏋滆礬寰勪笉瀛樺湪鐨勮瘽鏄棤絀峰ぇ銆?Dijstra綆楁硶鐨勫熀紜鎿嶄綔鏄竟鐨勬嫇灞曪細濡傛灉瀛樺湪涓鏉′粠u鍒?i>v鐨勮竟錛岄偅涔堜粠s鍒?i>u鐨勬渶鐭礬寰勫彲浠ラ氳繃灝嗚竟(u,v)娣誨姞鍒板熬閮ㄦ潵鎷撳睍涓鏉′粠s鍒皏鐨勮礬寰勩傝繖鏉¤礬寰勭殑闀垮害鏄痙[u]+w(u,v)銆傚鏋滆繖涓兼瘮鐩墠宸茬煡鐨?i>d[v]鐨勫艱灝忥紝鎴戜滑鍙互鐢ㄦ柊鍊兼潵鏇夸唬褰撳墠d[v]涓殑鍊箋傛嫇灞曡竟鐨勬搷浣滀竴鐩存墽琛屽埌鎵鏈夌殑d[v]閮戒唬琛ㄤ粠s鍒皏鏈鐭礬寰勭殑鑺辮垂銆傝繖涓畻娉曠粡榪囩粍緇囧洜鑰屽綋d[u]杈懼埌瀹冩渶緇堢殑鍊肩殑鏃跺欐病鏉¤竟(u,v)閮藉彧琚嫇灞曚竴嬈°?br />
綆楁硶嫻佺▼錛?br />1. 鍦ㄧ畻娉曚腑姣忎釜緇撶偣涓兘榪涜鏍囨敞錛屾爣娉ㄥ垎涓?font color="#ff0000">涓存椂鎬ф爣娉?/font>鍜?font color="#ff0000">姘鎬箙鎬ф爣娉?/font>錛?
2.鍒濆鏃?/font>錛屾墍鏈夌粨鐐歸兘涓?font color="#ff0000">涓存椂鎬ф爣娉?/font>錛?font color="#ff0000">鏍囨敞鍊間負鏃犵┓澶?/font>錛?br />3.灝?font color="#ff0000">婧愮粨鐐?/font>鏍囨敞涓?錛屼笖涓烘案涔呮ф爣娉紝騫朵護鍏朵負宸ヤ綔緇撶偣錛?br />4.媯鏌ヤ笌宸ヤ綔緇撶偣鐩擱偦騫舵爣娉ㄤ負涓存椂鏍囨敞鐨?/font>緇撶偣錛?font color="#ff0000">鑻ヨ緇撶偣鍒板伐浣滅粨鐐圭殑璺濈涓庡伐浣滅粨鐐圭殑鏍囨敞涔嬪拰灝忎簬璇ョ粨鐐圭殑鏍囨敞錛屽垯鐢ㄦ柊璁$畻寰楀埌鐨勫拰閲嶆柊鏍囨敞璇ョ粨鐐癸紝騫跺皢宸ヤ綔緇撶偣璁板綍涓鴻緇撶偣鐨勪笂涓緇撶偣錛?br />5.鍦?/font>鏁翠釜鍥?/font>涓煡鎵懼叿鏈夋渶灝忓肩殑涓存椂鎬ф爣娉ㄧ粨鐐癸紝灝嗗叾鍙樹負姘鎬箙鎬х粨鐐癸紝騫舵垚涓轟笅涓杞鏌ョ殑宸ヤ綔緇撶偣錛?br />閲嶅絎洓銆佷簲姝ワ紝鐩村埌鐩殑緇撶偣鎴愪負宸ヤ綔緇撶偣銆傝繖鏃剁洰鏍囩粨鐐逛腑鐨勬爣娉ㄥ煎氨鏄洰鏍囩粨鐐瑰埌婧愮粨鐐圭殑鏈鐭礬寰勫箋傝屽洖婧?font color="#0000ff">鍚勭粨鐐圭殑涓婁竴緇撶偣鐩村埌婧愮粨鐐廣傚氨鏄渶鐭礬寰勩?br />
紺轟緥錛?br />

鏂囩珷璧勬簮鏉ユ簮浜庯細
1. http://www.roboticfan.com/college/knowledge/200608/195.shtml
2. http://johnfat.bokee.com/3435427.html



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20涓栫邯鏈濂界殑10涓畻娉?杞澆)---浠嬬粛浜嗙編鍥界瀛﹀璇勫嚭鐨?0涓畻娉曪紝鎰熷叴瓚e彲浠ョ湅涓鐪?/title><link>http://m.shnenglu.com/ningfangli-blog/articles/15595.html</link><dc:creator>ningfangli</dc:creator><author>ningfangli</author><pubDate>Thu, 23 Nov 2006 12:51:00 GMT</pubDate><guid>http://m.shnenglu.com/ningfangli-blog/articles/15595.html</guid><wfw:comment>http://m.shnenglu.com/ningfangli-blog/comments/15595.html</wfw:comment><comments>http://m.shnenglu.com/ningfangli-blog/articles/15595.html#Feedback</comments><slash:comments>0</slash:comments><wfw:commentRss>http://m.shnenglu.com/ningfangli-blog/comments/commentRss/15595.html</wfw:commentRss><trackback:ping>http://m.shnenglu.com/ningfangli-blog/services/trackbacks/15595.html</trackback:ping><description><![CDATA[ <p align="center"> <font face="瀹嬩綋"> <span lang="EN-US">20</span>涓栫邯鏈濂界殑<span lang="EN-US">10</span>涓畻娉?/font> </p> <p align="center"> <font face="瀹嬩綋">涓夐暅鍏堢敓</font> </p> <p> <font face="瀹嬩綋">涓銆佺畻娉曚竴璇嶇殑鏉ユ簮</font> </p> <p> <font face="瀹嬩綋">銆銆<span lang="EN-US">Algos</span>鏄笇鑵婂瓧錛屾剰鎬濇槸<span lang="EN-US">鈥?/span>鐤?span lang="EN-US">鈥?/span>錛?span lang="EN-US">A1gor</span>鏄媺涓佸瓧錛屾剰鎬濇槸<span lang="EN-US">鈥?/span>鍐峰嵈<span lang="EN-US">鈥?/span>銆傝繖涓や釜瀛楅兘涓嶆槸<span lang="EN-US">A1gorithm(</span>綆楁硶<span lang="EN-US">)</span>涓璇嶇殑璇嶆牴錛?span lang="EN-US">a1gorithm</span>涓璇嶅嵈涓?span lang="EN-US">9</span>涓栫邯鐨勯樋鎷変集瀛﹁?span lang="EN-US">al-Khwarizmi</span>鏈夊叧錛屼粬鍐欑殑涔︺?span lang="EN-US">al-jabr w鈥檃l muqabalah</span>銆?span lang="EN-US">(</span>浠f暟瀛?span lang="EN-US">)</span>婕斿彉鎴愪負鐜板湪涓鐨勪唬鏁版暀縐戜功銆?span lang="EN-US">Ad-Khwarizmi</span>寮鴻皟姹傝В闂鐨勬湁鏉$悊鐨勬楠ゃ傚鏋滀粬鑳芥椿鍒頒粖澶╃殑璇濓紝浠栦竴瀹氫細琚互浠栫殑鍚嶅瓧鑰屽緱鍚嶇殑鏂規硶鐨勮繘灞曟墍鎰熷姩銆?/font> </p> <p> <font face="瀹嬩綋">浜屻?span lang="EN-US">20</span>涓栫邯<span lang="EN-US">10</span>鏈濂界殑綆楁硶</font> </p> <p> <font face="瀹嬩綋">銆銆<span lang="EN-US">20</span>涓栫邯鏈濂界殑綆楁硶錛岃綆楁満鏃朵唬鐨勬寫閫夋爣鍑嗘槸瀵圭瀛﹀拰宸ョ▼鐨勭爺絀跺拰瀹炶返褰卞搷鏈澶с備笅闈㈠氨鏄寜騫翠唬嬈″簭鎺掑垪鐨?span lang="EN-US">20</span>涓栫邯鏈濂界殑<span lang="EN-US">10</span>涓畻娉曘?span lang="EN-US"></span></font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">1.聽 Monte Carlo</span>鏂規硶</font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽1946</span>騫達紝鍦ㄦ礇鏂樋鎷夎帿鏂瀛﹀疄楠屽宸ヤ綔鐨?span lang="EN-US">John von Neumann</span>錛?span lang="EN-US">Stan Ulam</span>鍜?span lang="EN-US">Nick Metropolis</span>緙栧埗浜?span lang="EN-US">Metropolis</span>綆楁硶錛屼篃縐頒負<span lang="EN-US">Monte Carlo</span>鏂規硶銆?span lang="EN-US">Metropolis</span>綆楁硶鏃ㄥ湪閫氳繃妯′豢闅忔満榪囩▼錛屾潵寰楀埌鍏鋒湁闅句互鎺у埗鐨勫ぇ閲忕殑鑷敱搴︾殑鏁板奸棶棰樺拰鍏鋒湁闃朵箻瑙勬ā鐨勭粍鍚堥棶棰樼殑榪戜技瑙f硶銆傛暟瀛楄綆楁満鏄‘瀹氭ч棶棰樼殑璁$畻鐨勫己鏈夊姏</font> <span lang="EN-US"> <br /> </span> <font face="瀹嬩綋">宸ュ叿錛屼絾鏄浜庨殢鏈烘э紙涓嶇‘瀹氭э級闂濡備綍褰撴椂騫朵笉鐭ユ檽錛?span lang="EN-US">Metropolis</span>綆楁硶鍙互璇存槸鏈鏃╃殑鐢ㄦ潵鐢熸垚闅忔満鏁幫紝瑙e喅涓嶇‘瀹氭ч棶棰樼殑綆楁硶涔嬩竴銆?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">2.聽 </span>綰挎ц鍒掔殑鍗曠函褰㈡柟娉?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1947</span>騫達紝鍏板痙鍏徃鐨?span lang="EN-US">Grorge Dantzig</span>鍒涢犱簡綰挎ц鍒掔殑鍗曠函褰㈡柟娉曘傚氨鍏跺箍娉涚殑搴旂敤鑰岃█錛?span lang="EN-US">Dantzig</span>綆楁硶涓鐩存槸鏈鎴愬姛鐨勭畻娉曚箣涓銆傜嚎鎬ц鍒掑浜庨偅浜涜鎯沖湪緇忔祹涓婄珯浣忚剼錛屽悓鏃跺張鏈夎禆浜庢槸鍚﹀叿鏈夊湪棰勭畻鍜屽叾浠栫害鏉熸潯浠朵笅杈懼埌鏈浼樺寲鐨勮兘鍔涚殑宸ヤ笟鐣岋紝鏈夌潃鍐沖畾鎬х殑褰卞搷<span lang="EN-US">(</span>褰撶劧錛屽伐涓氫腑鐨?span lang="EN-US">鈥?/span>瀹為檯<span lang="EN-US">鈥?/span>闂寰寰鏄潪綰挎х殑錛涗嬌鐢ㄧ嚎鎬ц鍒掓湁鏃跺欐槸鐢變簬浼拌鐨勯綆楋紝浠庤岀畝鍖栦簡妯″瀷鑰屼績鎴愮殑<span lang="EN-US">)</span>銆傚崟綰艦娉曟槸涓縐嶈兘杈懼埌鏈浼樿В鐨勭簿緇嗙殑鏂規硶銆傚敖綆$悊璁轟笂璁插叾鏁堟灉鏄寚鏁拌“鍑忕殑錛屼絾鍦ㄥ疄璺典腑璇ョ畻娉曟槸楂樺害鏈夋晥鐨?span lang="EN-US">鈥斺?/span>瀹冩湰韜鏄庝簡鏈夊叧璁$畻鐨勬湰璐ㄧ殑涓浜涙湁瓚g殑浜嬫儏銆?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">3.聽 Krylov</span>瀛愮┖闂村彔浠f硶</font> </p> <p style="TEXT-INDENT: 24pt"> <font face="瀹嬩綋"> <span lang="EN-US">1950</span>騫達紝鏉ヨ嚜緹庡浗鍥藉鏍囧噯灞鐨勬暟鍊煎垎鏋愮爺絀舵墍鐨?span lang="EN-US">Magnus Hestenes, Eduard Stiefel</span>鍜?span lang="EN-US">Cornelius Lanczos</span>寮鍒涗簡<span lang="EN-US">Krylov</span>瀛愮┖闂村彔浠f硶鐨勭爺鍒躲傝繖浜涚畻娉曞鐞嗙湅浼肩畝鍗曠殑姹傝В褰負<span lang="EN-US">聽聽聽</span></font> </p> <p style="TEXT-INDENT: 24pt" align="center"> <span lang="EN-US"> <font face="瀹嬩綋">Ax=b</font> </span> </p> <p style="TEXT-INDENT: 24pt"> <font face="瀹嬩綋">鐨勬柟紼嬬殑闂銆傚綋鐒墮殣钘忕殑鍥伴毦鍦ㄤ簬<span lang="EN-US">A</span>鏄竴涓法鍨嬬殑<span lang="EN-US">n*n </span>鐭╅樀錛岃嚧浣夸唬鏁拌В<span lang="EN-US">聽聽</span></font> </p> <p style="TEXT-INDENT: 24pt" align="center"> <span lang="EN-US"> <font face="瀹嬩綋">x=b/A </font> </span> </p> <p style="TEXT-INDENT: 24pt"> <font face="瀹嬩綋">鏄笉瀹規槗璁$畻鐨?span lang="EN-US">(</span>紜疄錛岀煩闃電殑<span lang="EN-US">鈥?/span>鐩擱櫎<span lang="EN-US">鈥?/span>涓嶆槸涓涓疄闄呬笂鏈夌敤鐨勬蹇?span lang="EN-US">)</span>銆傚彔浠f硶<span lang="EN-US">鈥斺?/span>璇稿姹傝В褰負<br /><br /></font> </p> <p style="TEXT-INDENT: 24pt" align="left"> <font face="瀹嬩綋"> <span lang="EN-US">Kx(k+1)=Kx(k)+b-Ax(k)<br /></span> <br />鐨勬柟紼嬶紝鍏朵腑<span lang="EN-US">K </span>鏄竴涓悊鎯沖湴<span lang="EN-US">鈥?/span>鎺ヨ繎<span lang="EN-US">鈥滱 </span>鐨勮緝涓虹畝鍗曠殑鐭╅樀<span lang="EN-US">鈥斺?/span>瀵艱嚧浜?span lang="EN-US">Krylov</span>瀛愮┖闂寸殑鐮旂┒銆備互淇勭綏鏂暟瀛﹀<span lang="EN-US">Nikolai Krylov</span>鍛藉悕鐨?span lang="EN-US">Krylov</span>瀛愮┖闂寸敱浣滅敤鍦ㄥ垵濮?span lang="EN-US">鈥?/span>浣欓噺<span lang="EN-US">鈥?/span>鍚戦噺</font> </p> <p style="TEXT-INDENT: 24pt"> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽 r(0)=b-Ax(0)<br /></span>涓婄殑鐭╅樀騫傚紶鎴愮殑銆傚綋<span lang="EN-US"> A</span>鏄縐扮煩闃墊椂錛?span lang="EN-US">Lanczos</span>鎵懼埌浜嗕竴縐嶇敓鎴愯繖縐嶅瓙絀洪棿鐨勬浜ゅ熀鐨勬瀬濂界殑鏂規硶銆傚浜庡縐版瀹氱殑鏂圭▼緇勶紝<span lang="EN-US">Hestenes </span>鍜?span lang="EN-US">Stiefel</span>鎻愬嚭浜嗙О涓哄叡杞搴︽硶鐨勭敋鑷蟲洿濡欑殑鏂規硶銆傝繃鍘葷殑<span lang="EN-US">50</span>騫翠腑錛岃澶氱爺絀朵漢鍛樻敼榪涘茍鎵╁睍浜嗚繖浜涚畻娉曘傚綋鍓嶇殑涓濂楁柟娉曞寘鎷潪瀵圭О鏂圭▼緇勭殑姹傝В鎶宸э紝鍍忓瓧棣栫緝鎷艱瘝涓?span lang="EN-US">GMRES</span>鍜?span lang="EN-US">Bi-CGSTAB</span>閭f牱鐨勭畻娉曘?span lang="EN-US">(GMRES</span>鍜?span lang="EN-US">Bi-CGSTAB</span>鍒嗗埆棣栨鍑虹幇浜?span lang="EN-US">1986</span>鍜?span lang="EN-US">1992聽 SIAM journal on Scientific and Statistical computing(</span>緹庡浗宸ヤ笟涓庡簲鐢ㄦ暟瀛﹀浼氱殑縐戝鍜岀粺璁¤綆楁潅蹇?span lang="EN-US">)</span>銆?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">4.聽 </span>鐭╅樀璁$畻鐨勫垎瑙f柟娉?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽1951</span>騫達紝姍℃爲宀浗瀹跺疄楠屽鐨?span lang="EN-US">A1ston Householder</span>緋葷粺闃愯堪浜嗙煩闃佃綆楃殑鍒嗚В鏂規硶銆傜爺絀惰瘉鏄庤兘鎶婄煩闃靛洜瀛愬垎瑙d負涓夎銆佸瑙掋佹浜ゅ拰鍏朵粬鐗規畩褰㈠紡鐨勭煩闃墊槸鏋佸叾鏈夌敤鐨勩傝繖縐嶅垎瑙f柟娉曚嬌杞歡鐮旂┒浜哄憳鑳界敓浜у嚭鐏墊椿鏈夋晥鐨勭煩闃佃蔣浠跺寘銆傝繖涔熶績榪涗簡鏁板肩嚎鎬т唬鏁頒腑鍙嶅鍑虹幇鐨勫ぇ闂涔嬩竴鐨勮垗鍏ヨ宸垎鏋愰棶棰樸?span lang="EN-US"> (1961</span>騫翠雞鏁﹀浗瀹剁墿鐞嗗疄楠屽鐨?span lang="EN-US">James Wilkinson</span>鍩轟簬鎶婄煩闃靛垎瑙d負涓嬪拰涓婁笁瑙掔煩闃靛洜瀛愮殑縐殑<span lang="EN-US">LU</span>鍒嗚В錛屽湪緹庡浗璁$畻鏈哄崗浼?span lang="EN-US">(ACM)</span>鐨勬潅蹇椾笂鍙戣〃浜嗕竴綃囬涓?span lang="EN-US">鈥?/span>鐭╅樀閫嗙殑鐩存帴鏂規硶鐨勮宸垎鏋?span lang="EN-US">鈥?/span>鐨勯噸瑕佹枃绔犮?span lang="EN-US">)</span></font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">5.聽 Fortran</span>鏈浼樼紪璇戠▼搴?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1957</span>騫達紝<span lang="EN-US">John Backus</span>鍦?span lang="EN-US">IBM</span>棰嗗涓涓皬緇勭爺鍒?span lang="EN-US">Fortran</span>鏈浼樼紪璇戠▼搴忋?/font> <span lang="EN-US"> <br /> <font face="瀹嬩綋">Fortran</font> </span> <font face="瀹嬩綋">鐨勫垱閫犲彲鑳芥槸璁$畻鏈虹紪紼嬪巻鍙蹭笂鐙竴鏃犱簩鐨勬渶閲嶈鐨勪簨浠訛細縐戝瀹?span lang="EN-US">(</span>鍜屽叾浠栦漢<span lang="EN-US">)</span>緇堜簬鍙互鏃犻渶渚濋潬鍍忓湴鐙遍偅鏍峰彲鎬曠殑鏈哄櫒浠g爜錛屽氨鍙憡璇夎綆楁満浠栦滑鎯寵鍋氫粈涔堛傝櫧鐒剁幇浠g紪璇戠▼搴忕殑鏍囧噯騫朵笉榪囧垎<span lang="EN-US">鈥曗旻ortran I</span>鍙寘鍚?span lang="EN-US">23</span>錛?span lang="EN-US">500</span>鏉℃眹緙栬璦鎸囦護<span lang="EN-US">鈥曗?/span>鏃╂湡鐨勭紪璇戠▼搴忎粛鐒惰兘瀹屾垚浠や漢鍚冩儕鐨勫鏉傝綆椼傚氨鍍?span lang="EN-US">Backus</span>鏈漢鍦?span lang="EN-US">1998</span>騫村湪<span lang="EN-US">IEEE annals of the History of computing </span>鍙戣〃鐨勬湁鍏?span lang="EN-US">Fortran I</span>錛?span lang="EN-US">II, III</span>鐨勮繎浠e巻鍙茬殑鏂囩珷涓洖蹇嗛亾錛氱紪璇戠▼搴?span lang="EN-US">鈥?/span>鎵浜х敓鐨勫姝ゆ湁鏁堢殑浠g爜錛屼嬌寰楀叾杈撳嚭浠ょ爺絀跺畠鐨勭紪紼嬩漢鍛橀兘鎰熷埌鍚撲簡涓璺熾?span lang="EN-US">鈥?/span></font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">6.聽 </span>鐭╅樀鏈緛鍊艱綆楃殑<span lang="EN-US">QR</span>綆楁硶</font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1959鈥?1</span>騫達紝浼︽暒<span lang="EN-US">Ferranti Ltd.</span>鐨?span lang="EN-US">J.G. F. Francis</span>鎵懼埌浜嗕竴縐嶇О涓?span lang="EN-US">QR</span>綆楁硶鐨勮綆楁湰寰佸肩殑紼沖畾鐨勬柟娉曘傛湰寰佸煎ぇ姒傛槸鍜岀煩闃電浉榪炲湪<span lang="EN-US">鈥?/span>璧風殑鏈閲嶈鐨勬暟浜嗭紝鑰屼笖璁$畻瀹冧滑鍙兘鏄渶闇瑕佹妧宸х殑銆傛妸<span lang="EN-US">鈥?/span>涓柟闃靛彉鎹負涓涓?span lang="EN-US">鈥?/span>鍑犱箮鏄?span lang="EN-US">鈥?/span>涓婁笁瑙掔殑鐭╅樀<span lang="EN-US">鈥曗?/span>鎰忓嵆鍦ㄧ揣鎸ㄧ潃鐭╅樀涓誨瑙掔嚎涓嬮潰鐨勪竴鏂滃垪涓婂彲鑳芥湁闈為浂鍏冪礌<span lang="EN-US">鈥曗?/span>鏄浉瀵瑰鏄撶殑錛屼絾瑕佹兂涓嶄駭鐢熷ぇ閲忕殑璇樊灝辨妸榪欎簺闈為浂鍏冪礌娑堝幓錛屽氨涓嶆槸騫沖嚒鐨勪簨浜嗐?span lang="EN-US">QR </span>綆楁硶姝eソ鏄兘杈懼埌榪欎竴鐩殑鐨勬柟娉曪紝鍩轟簬<span lang="EN-US">QR </span>鍒嗚В錛?span lang="EN-US"> A</span>鍙互鍐欐垚</font> <span lang="EN-US"> <br /> </span> <font face="瀹嬩綋">姝d氦鐭╅樀<span lang="EN-US">Q </span>鍜屼竴涓笁瑙掔煩闃?span lang="EN-US">R </span>鐨勪箻縐紝榪欑鏂規硶鍙犱唬鍦版妸</font> <font face="瀹嬩綋"> <span lang="EN-US">聽A=Q(k)R(k)<br /></span>鍙樻垚<span lang="EN-US">A(k+1)==Q(k)R(k) </span>灝卞姞閫熸敹鏁涘埌涓婁笁瑙掔煩闃佃岃█澶氬皯鏈夌偣涓嶈兘鎸囨湜銆?span lang="EN-US">20</span>涓栫邯<span lang="EN-US">60</span>騫翠唬涓湡<span lang="EN-US">QR </span>綆楁硶鎶婁竴搴﹂毦浠ュ浠樼殑鏈緛鍊奸棶棰樺彉鎴愪簡渚嬭紼嬪簭鐨勮綆椼?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">7.聽 </span>蹇熷垎綾繪硶</font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽1962</span>錛氫雞鏁?span lang="EN-US">Elliott Brothers, Ltd.</span>鐨?span lang="EN-US">Tony Hoare</span>鎻愬嚭浜嗗揩閫?span lang="EN-US">(</span>鎸夊ぇ灝?span lang="EN-US">)</span>鍒嗙被娉?/font> <font face="瀹嬩綋"> <span lang="EN-US">.</span>鎶?span lang="EN-US">n</span>涓簨鐗╂寜鏁版垨瀛楁瘝鐨勬搴忔帓鍒楄搗鏉ワ紝鍦ㄥ績鏅轟笂鏄笉浼氭湁浠涔堣Е鍔ㄧ殑鍗曡皟騫沖嚒鐨勪簨銆傛櫤鍔涚殑鎸戞垬鍦ㄤ簬鍙戞槑涓縐嶅揩閫熷畬鎴愭帓搴忕殑鏂規硶銆?span lang="EN-US">Hoare</span>鐨勭畻娉曞埄鐢ㄤ簡鍙よ佺殑鍒嗗壊寮鍜屾帶鍒剁殑閫掑綊絳栫暐鏉ヨВ鍐抽棶棰橈細鎸戜竴涓厓绱犱綔涓?span lang="EN-US">鈥?/span>涓誨厓<span lang="EN-US">鈥?/span>銆佹妸鍏朵綑鐨勫厓绱犲垎鎴?span lang="EN-US">鈥?/span>澶х殑<span lang="EN-US">鈥?/span>鍜?span lang="EN-US">鈥?/span>灝忕殑<span lang="EN-US">鈥?/span>涓ゅ爢</font> <span lang="EN-US"> <br /> <font face="瀹嬩綋">(</font> </span> <font face="瀹嬩綋">褰撳拰涓誨厓姣旇緝鏃?span lang="EN-US">)</span>銆佸啀鍦ㄦ瘡涓鍫嗕腑閲嶅榪欎竴榪囩▼銆傚敖綆″彲鑳借鍋氬彈鍒頒弗鍘夎矗澶囩殑鍋氬畬鍏ㄩ儴<span lang="EN-US">N(N-1)/2 </span>嬈$殑姣旇緝<span lang="EN-US">(</span>鐗瑰埆鏄紝濡傛灉浣犳妸涓誨厓浣滀負鏃╁凡鎸夊ぇ灝忓垎綾誨ソ鐨勮〃鍒楃殑絎竴涓厓绱犵殑</font> <span lang="EN-US"> <br /> </span> <font face="瀹嬩綋">璇濓紒<span lang="EN-US">)</span>錛屽揩閫熷垎綾繪硶榪愯鐨勫鉤鍧囨鏁板叿鏈?span lang="EN-US">O(Nlog(N)) </span>鐨勬湁鏁堟э紝鍏朵紭緹庣殑綆媧佹т嬌涔嬫垚涓鴻綆楀鏉傛х殑钁楀悕鐨勪緥瀛愩?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">8.聽 </span>蹇?span lang="EN-US">Fourier</span>鍙樻崲</font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1965</span>騫達紝<span lang="EN-US">IBM</span>鐨?span lang="EN-US">T. J. Watson</span>鐮旂┒涓績鐨?span lang="EN-US">James Cooley</span>浠ュ強鏅灄鏂】澶у鍜?span lang="EN-US">AT</span>錛?span lang="EN-US">T</span>璐濆皵瀹為獙瀹ょ殑<span lang="EN-US">John Tukey</span>鍚戝叕浼楅忛湶浜嗗揩閫?span lang="EN-US">Fourier</span>鍙樻崲<span lang="EN-US">(</span>鏂規硶<span lang="EN-US">)(FFT)</span>銆傚簲鐢ㄦ暟瀛︿腑鎰忎箟鏈娣辮繙鐨勭畻娉曪紝鏃犵枒鏄嬌淇″彿澶勭悊瀹炵幇紿佺牬鎬ц繘灞曠殑<span lang="EN-US">FFT</span>銆傚叾鍩烘湰鎬濇兂瑕佽拷</font> <span lang="EN-US"> <br /> </span> <font face="瀹嬩綋">婧埌<span lang="EN-US">Gauss(</span>浠栭渶瑕佽綆楀皬琛屾槦鐨勮建閬?span lang="EN-US">)</span>錛屼絾鏄?span lang="EN-US">Cooley鈥擳ukey</span>鐨勮鏂囧紕娓呮浜?span lang="EN-US">Fourier</span>鍙樻崲璁$畻璧鋒潵鏈夊瀹規槗銆傚氨鍍忓揩閫熷垎綾繪硶涓鏍鳳紝<span lang="EN-US">FFT</span>鏈夎禆浜庣敤鍒嗗壊寮鍜屾帶鍒剁殑絳栫暐錛屾妸琛ㄩ潰涓婁護浜鴻鍘岀殑<span lang="EN-US">O(N*N) </span>闄嶅埌浠や漢嬈箰鐨?span lang="EN-US">O(Nlog(N)) </span>銆備絾鏄笉鍍忓揩閫熷垎綾繪硶錛屽叾鎵ц<span lang="EN-US">(</span>鍒濅竴鐪?span lang="EN-US">)</span>鏄潪鐩磋鐨勮屼笖涓嶉偅涔堢洿鎺ャ傚叾鏈韓灝辯粰璁$畻鏈虹瀛︿竴縐嶆帹鍔ㄥ姏鍘葷爺絀惰綆楅棶棰樺拰綆楁硶鐨勫浐鏈夊鏉傛с?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">9.聽 </span>鏁存暟鍏崇郴渚︽煡綆楁硶</font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1977</span>騫達紝<span lang="EN-US">BrighamYoung</span>澶у鐨?span lang="EN-US">Helaman Ferguson </span>鍜?span lang="EN-US">Rodney Forcade</span>鎻愬嚭浜嗘暣鏁板叧緋諱睛鏌ョ畻娉曘傝繖鏄竴涓彜鑰佺殑闂錛氱粰瀹?span lang="EN-US">鈥?/span>緇勫疄鏁幫紝渚嬪璇?span lang="EN-US">x(1),x(2),...,x(n) </span>錛屾槸鍚﹀瓨鍦ㄦ暣鏁?span lang="EN-US">a(1),a(2),..,a(n) </span>錛堜笉鍏ㄤ負闆訛級錛屼嬌寰?/font> <span lang="EN-US"> <br /> <font face="瀹嬩綋">聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽聽 a(1)x(1)+a(2)x(2)+...+a(n)x(n)=0<br /></font> </span> <font face="瀹嬩綋">瀵逛簬<span lang="EN-US">n=2 </span>錛屽巻鍙叉偁涔呯殑嬈у嚑閲屽緱綆楁硶鑳藉仛榪欓」宸ヤ綔銆佽綆?span lang="EN-US">x(1)/x(2) </span>鐨勮繛鍒嗘暟灞曞紑涓殑鍚勯」銆傚鏋?span lang="EN-US">x(1)/x(2) </span>鏄湁鐞嗘暟錛屽睍寮浼氱粓姝紝鍦ㄩ傚綋灞曞紑鍚庡氨緇欏嚭浜?span lang="EN-US">鈥?/span>鏈灝忕殑<span lang="EN-US">鈥?/span>鏁存暟<span lang="EN-US">a(1)聽</span>鍜?span lang="EN-US">a(2) </span>銆傛鍑犻噷寰楃畻娉曚笉緇堟<span lang="EN-US">鈥斺?/span>鎴栬呭鏋滀綘鍙槸綆鍗曞湴鐢變簬鍘屽﹁綆?span lang="EN-US">鈥斺?/span>閭d箞灞曞紑鐨勮繃紼嬭嚦灝戞彁渚涗簡鏈灝忔暣鏁板叧緋葷殑澶у皬鐨勪笅鐣屻?span lang="EN-US">Ferguson</span>鍜?span lang="EN-US">Forcade</span>鐨勬帹騫挎洿鏈夊▉鍔涳紝灝界榪欑鎺ㄥ箍鏇撮毦浜庢墽琛?span lang="EN-US">(</span>鍜岀悊瑙?span lang="EN-US">)</span>銆備緥濡傦紝浠栦滑鐨勪睛鏌ョ畻娉曡鐢ㄦ潵姹傚緱閫昏緫鏂皼<span lang="EN-US">(logistic)</span>鏄犲皠鐨勭涓夊拰絎洓涓垎姝х偣錛?span lang="EN-US">b(3)=3.544090 </span>鍜?span lang="EN-US"> b(4)=3.564407</span>鎵婊¤凍鐨勫欏瑰紡鐨勭簿紜郴鏁般?span lang="EN-US">(</span>鍚庤呮槸<span lang="EN-US">120 </span>闃剁殑澶氶」寮忥紱瀹冪殑鏈澶х殑緋繪暟鏄?span lang="EN-US">257^30 </span>銆?span lang="EN-US">)</span>宸茶瘉鏄庤綆楁硶鍦ㄧ畝鍖栭噺瀛愬満璁轟腑鐨?span lang="EN-US">Feynman</span>鍥劇殑璁$畻涓槸鏈夌敤鐨勩?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">10. </span>蹇熷鏋佺畻娉?/font> </p> <p> <font face="瀹嬩綋"> <span lang="EN-US">聽聽聽 1987</span>騫達紝鑰墮瞾澶у鐨?span lang="EN-US">Leslie Greengard </span>鍜?span lang="EN-US">Vladimir Rokhlin</span>鍙戞槑浜嗗揩閫熷鏋佺畻娉曘?/font> <font face="瀹嬩綋">璇ョ畻娉曞厠鏈嶄簡<span lang="EN-US">N</span>浣撴ā鎷熶腑鏈浠や漢澶寸柤鐨勫洶闅句箣涓錛氱粡鐢卞紩鍔涙垨闈欑數鍔涚浉浜掍綔鐢ㄧ殑<span lang="EN-US">N</span>涓矑瀛愯繍鍔ㄧ殑綺劇‘璁$畻<span lang="EN-US">(</span>鎯寵薄涓涓嬮摱娌崇郴涓殑鏄熶綋錛屾垨鑰呰泲鐧借川涓殑鍘熶簬<span lang="EN-US">)</span>鐪嬫潵闇瑕?span lang="EN-US">O(N*N) </span>鐨勮綆楅噺</font> <span lang="EN-US"> <br /> <font face="瀹嬩綋">鈥斺?/font> </span> <font face="瀹嬩綋">姣旇緝姣忎竴瀵硅川鐐歸渶瑕佷竴嬈¤綆椼傝綆楁硶鍒╃敤澶氭瀬灞曞紑<span lang="EN-US">(</span>鍑鐢佃嵎鎴栬川閲忋佸伓鏋佺煩銆佸洓鐭╋紝絳夌瓑<span lang="EN-US">)</span>鏉ヨ繎浼奸仴榪滅殑涓緇勮川鐐瑰褰撳湴涓緇勮川鐐圭殑褰卞搷銆傜┖闂寸殑灞傛鍒嗚В鐢ㄦ潵紜畾褰撹窛紱誨澶ф椂錛屾瘮浠ュ線浠諱綍鏃跺欓兘鏇村ぇ鐨勮川鐐圭粍銆傚揩閫熷鏋佺畻娉曠殑涓涓槑鏄句紭鐐規槸鍏鋒湁涓ユ牸鐨勮宸及璁★紝榪欐槸璁稿綆楁硶鎵緙哄皯鐨勬ц川銆?/font> </p> <p> <font face="瀹嬩綋">涓夈佺粨鏉熻</font> <span lang="EN-US"> <br /> <font face="瀹嬩綋">聽聽聽 <br /></font> </span> <font face="瀹嬩綋">銆銆<?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" /?><st1:chmetcnv tcsc="0" numbertype="1" negative="False" hasspace="False" sourcevalue="2" unitname="l" w:st="on"><span lang="EN-US">2l</span></st1:chmetcnv>涓栫邯灝嗕細甯︽潵浠涔堟牱鐨勬柊鐨勬礊瀵熷拰綆楁硶錛熷浜庡張涓涓竴鐧懼勾瀹屾暣鐨勫洖絳旀樉鐒舵槸涓嶇煡閬撶殑銆傜劧鑰岋紝鏈変竴鐐逛技涔庢槸鑲畾鐨勩傛濡?span lang="EN-US">20</span>涓栫邯鑳藉浜х敓鏈濂界殑<span lang="EN-US">l0</span>涓畻娉曚竴鏍鳳紝鏂頒笘綰鎴戜滑鏉ヨ鏃笉浼氭槸寰堝畞闈欑殑錛屼篃涓嶄細鏄急鏅虹殑銆?/font> </p> <img src 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