2021骞�婀栧崡甯寖澶у(xu茅)纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│鑷懡椤岀鐩€冭│澶х侗

鑰冭│绉戠洰浠ｇ⒓锛�723            鑰冭│绉戠洰鍚嶇ū锛氭暩(sh霉)瀛�(xu茅)鍒嗘瀽

涓€銆佽€冭│鍏�(n猫i)瀹瑰強瑕侀粸(di菐n)

1銆佹サ闄愯珫

鑰冭│鍏�(n猫i)瀹�

鈶�  鍚勭ó妤甸檺鐨勮▓(j矛)绠楋紱 鈶� 鍠(di脿o)鏈夌晫鏀舵杺鍘熺悊銆佽嚧瀵嗘€у畾鐞�銆佺⒑鐣屽師鐞�銆丆auchy鏀舵杺鍘熺悊绛夊(sh铆)鏁�(sh霉)鍩烘湰鐞嗚珫鐨勯潏娲绘噳(y墨ng)鐢�锛� 鈶� 閫ｇ簩(x霉)鍑芥暩(sh霉)鐗瑰垾鏄枆鍗€(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鎬ц唱(zh矛)鐨勯亱(y霉n)鐢�锛� 鈶� 妤甸檺瀹氱京鐨勭啛绶存帉鎻＄瓑.

鑰冭│瑕侀粸(di菐n)

锛�1锛夎兘鐔熺反瑷�(j矛)绠楀悇绋サ闄�锛屽寘鎷柈璁婇噺鍜屽璁婇噺鎯呭舰.

锛�2锛夎兘鐔熺反鍒╃敤鍏€�(g猫)瀵�(sh铆)鏁�(sh霉)鍩烘湰瀹氱悊灏ゅ叾鏄柈瑾�(di脿o)鏈夌晫鏀舵杺鍘熺悊銆佽嚧瀵嗘€у畾鐞�銆佺⒑鐣屽師鐞嗐€丆auchy鏀舵杺鍘熺悊閫�(j矛n)琛屽悇绋悊璜栬瓑鏄庯紟

锛�3锛夎兘鐔熺反鎺屾彙鍠畩閲忛€ｇ簩(x霉)鍑芥暩(sh霉)鐗瑰垾鏄枆鍗€(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勫悇绋€ц唱(zh矛)锛屽苟鑳藉埄鐢ㄩ€欎簺鎬ц唱(zh矛)閫�(j矛n)琛岃▓(j矛)绠楀拰璀夋槑锛涙帉鎻″璁婇噺閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)灏ゅ叾鏄湁鐣岄枆鍩熶笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛岃兘鍒╃敤閫欎簺鎬ц唱(zh矛)閫�(j矛n)琛岃▓(j矛)绠楀拰璀夋槑锛�

锛�4锛夌啛绶存帉鎻″悇绋サ闄愮殑瀹氱京锛屽苟鑳界敤閭忚集琛�(sh霉)瑾�(y菙)閫�(j矛n)琛岀悊璜栬瓑鏄�.

2銆佸柈璁婇噺寰垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹�

鈶�     寰垎涓€煎畾鐞嗭紙鍖呮嫭Roll瀹氱悊銆丩agrange涓€煎畾鐞�銆丆auchy涓€煎畾鐞嗙瓑锛�

鐨勯潏娲婚亱(y霉n)鐢紙鍖呮嫭鍠(di脿o)鎬ц◣璜栥€佹サ鍊肩殑姹傚彇銆佸嚫鍑规€у晱椤�銆佺瓑寮忓拰涓嶇瓑寮忕殑璀夋槑绛夛級锛� 鈶� Talor鍏紡鐨勯潏娲婚亱(y霉n)鐢紙鍖呮嫭鐢↙agrange浣欓爡(xi脿ng)褰㈠紡璀変笉绛夊紡銆佺敤Peano浣欓爡(xi脿ng)褰㈠紡浼拌▓(j矛)闅庝互鍙婃眰妤甸檺绛夛級锛涒憿 鍚勭ó褰㈠紡灏�(d菐o)鏁�(sh霉)鐨勮▓(j矛)绠楋紱 鈶� 灏�(d菐o)鏁�(sh霉)鐨勫畾缇╁拰閬�(y霉n)鐢ㄧ瓑.

鑰冭│瑕侀粸(di菐n)

锛�1锛夌啛绶存帉鎻″井鍒嗕腑鍊煎畾鐞�锛屽寘鎷琑oll瀹氱悊銆丩agrange涓€煎畾鐞�銆丆auchy涓€煎畾鐞嗙殑姊濅欢鍜岀祼(ji茅)璜�锛岃兘鐔熺反鍒╃敤閫欎簺瀹氱悊閫�(j矛n)琛岀悊璜栬瓑鏄庢垨瑷�(j矛)绠�锛屽寘鎷嚱鏁�(sh霉)鍠(di脿o)鎬ц◣璜�銆佹サ鍊肩殑姹傚彇銆佸嚫鍑规€у晱椤岀殑瑷庤珫銆佺瓑寮忓拰涓嶇瓑寮忕殑璀夋槑绛夛紟

锛�2锛� 鐔熺反鎺屾彙Talor鍏紡鐨勬浠跺拰绲�(ji茅)璜�锛屽苟鑳藉仛鍒伴潏娲婚亱(y霉n)鐢�锛屽挨鍏舵槸鍒╃敤Lagrange浣欓爡(xi脿ng)褰㈠紡璀変笉绛夊紡銆丳eano浣欓爡(xi脿ng)褰㈠紡浼拌▓(j矛)闅庝互鍙婃眰妤甸檺绛�.

锛�3锛夌啛绶存帉鎻″京(f霉)鍚堝嚱鏁�(sh霉)灏�(d菐o)鏁�(sh霉)鐨勮▓(j矛)绠楀拰楂橀殠灏�(d菐o)鏁�(sh霉)鐨勮▓(j矛)绠楋紟

锛�4锛夌啛绶存帉鎻″皫(d菐o)鏁�(sh霉)鐨勫畾缇╁拰鎬ц唱(zh矛)锛岃兘鐢ㄩ倧杓獮(y菙)瑷€閫�(j矛n)琛岀悊璜栬瓑鏄�锛岀啛绶存帉鎻″埄鐢ㄥ皫(d菐o)鏁�(sh霉)瀹氱京閫�(j矛n)琛岃瓑鏄庢垨瑷�(j矛)绠�.

3銆佸柈璁婇噺绌嶅垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹�

鈶�     鍚勭ó涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勭啛绶磋▓(j矛)绠�锛屽挨鍏舵槸瑷�(j矛)绠椾腑鐨勮檿鐞嗘妧宸�锛�  鈶� 寤ｇ京

绌嶅垎鐨勮▓(j矛)绠楀拰鏂傛暎鎬у垽鍒�锛� 鈶� 瀹氱⿳鍒嗙殑瀹氱京鍜屾€ц唱(zh矛)鐨勯潏娲婚亱(y霉n)鐢ㄧ瓑.

鑰冭│瑕侀粸(di菐n)

锛�1锛夌啛绶磋▓(j矛)绠楀悇绋笉瀹氱⿳鍒�銆佸畾绌嶅垎锛岀啛绶存帉鎻℃箠寰垎娉�銆佹彌鍏冩硶銆佸垎閮ㄧ⿳鍒嗘硶浠ュ強甯哥敤鐨勮▓(j矛)绠楁妧宸�锛岀啛绶存帉鎻″鍋跺嚱鏁�(sh霉)銆佸懆鏈熷嚱鏁�(sh霉)鐨勭⿳鍒嗙壒榛�(di菐n)锛�

 锛�2锛夌啛绶存帉鎻″唬缇╃⿳鍒嗙殑瑷�(j矛)绠楋紝鐔熺反鎺屾彙鍗€(q奴)闁撶劇(w煤)闄愬瀷銆佸嚱鏁�(sh霉)鐒�(w煤)鐣屽瀷浠ュ強娣峰悎鍨嬪唬缇╃⿳鍒嗙殑鏂傛暎鎬у垽鍒�锛屽苟鑳介€�(j矛n)琛岀悊璜栬瓑鏄庯紟

 锛�3锛夌啛绶存帉鎻″畾绌嶅垎鐨勫畾缇�锛岃兘鍒╃敤瀹氱⿳鍒嗙殑瀹氱京閫�(j矛n)琛屾サ闄愮殑瑷�(j矛)绠楋紝鐔熺反鎺屾彙瀹氱⿳鍒嗙殑鎬ц唱(zh矛)锛屽苟鑳藉埄鐢ㄩ€欎簺鎬ц唱(zh矛)閫�(j矛n)琛岀悊璜栬瓑鏄�锛屾帉鎻″父鐢ㄥ彲绌嶅嚱鏁�(sh霉)椤烇紟

4銆佺礆(j铆)鏁�(sh霉)璜�

鑰冭│鍏�(n猫i)瀹�

鈶�     鍚勭ó鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)灏ゅ叾鏄闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬杺鏁ｆ€у垽鍒�锛涒憽 鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬€ц唱(zh矛)

鈶� 鍑芥暩(sh霉)鍒楀拰鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勪竴鑷存敹鏂傛€у垽鍒�锛岀郸瀹氬嚱鏁�(sh霉)Fourier绱�(j铆)鏁�(sh霉)鐨勫睍闁嬪拰鐗规畩榛�(di菐n)鐨勬敹鏂傛€�锛涒懀鍑芥暩(sh霉)鍒楀拰鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)涓€鑷存敹鏂傛€ц唱(zh矛)鐨勯潏娲婚亱(y霉n)鐢� 锛涒懁鍐礆(j铆)鏁�(sh霉)鐨勬敹鏂傛€у拰灞曢枊绛夌煡璀�(sh铆)鐨勭啛绶存帉鎻�.

鑰冭│瑕侀粸(di菐n)

锛�1锛夌啛绶存帉鎻＄礆(j铆)鏁�(sh霉)鐨勬杺鏁ｆ€у垽鍒�锛屽挨鍏舵槸姝ｉ爡(xi脿ng)绱�(j铆)鏁�(sh霉)鍜屼氦閷�(cu貌)绱�(j铆)鏁�(sh霉)鏂傛暎鎬у垽鍒�.

锛�2锛夋帉鎻℃暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勪竴浜涘父鐢ㄦ€ц唱(zh矛)锛屽挨鍏舵槸绲曞皪(du矛)鏀舵杺绱�(j铆)鏁�(sh霉)鑸囨浠舵敹鏂傜祼(ji茅)鏉熺殑甯歌(gu墨)鎬ц唱(zh矛).

锛�3锛夌啛绶存帉鎻″嚱鏁�(sh霉)鍒楀拰鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)涓€鑷存敹鏂傛€х殑鍒ゅ垾锛屽挨鍏舵槸鐢ㄥ畾缇┿€佸劒(y艒u)绱�(j铆)鏁�(sh霉)鍒ゅ垾娉�銆丄bel鍒ゅ垾娉曘€丏irichlet鍒ゅ垾娉曞垽鍒ュ嚱鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勪竴鑷存敹鏂傛€�锛岀啛绶存帉鎻＄郸瀹氬嚱鏁�(sh霉)鐨凢ourier灞曢枊锛岃兘绲﹀嚭Fourier绱�(j铆)鏁�(sh霉)鍦ㄧ壒娈婇粸(di菐n)鐨勬敹鏂傛€�.

锛�4锛夌啛绶存帉鎻″嚱鏁�(sh霉)鍒楀拰鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)涓€鑷存敹鏂傛€х殑鎬ц唱(zh矛)閬�(y霉n)鐢�锛屽寘鎷€ｇ簩(x霉)鎬�銆佸彲绌嶆€у拰鍙井鎬э紝鑳藉埄鐢ㄩ€欎簺鎬ц唱(zh矛)閫�(j矛n)琛岀悊璜栬瓑鏄�.

锛�5锛夌啛绶存帉鎻″啰绱�(j铆)鏁�(sh霉)鏀舵杺鍗€(q奴)闁撶殑姹傛硶锛岀啛绶存帉鎻″父瑕�(gu墨)鍑芥暩(sh霉)鐨勫啰绱�(j铆)鏁�(sh霉)灞曢枊锛屽苟鎺屾彙涓€浜涚壒娈婂啰绱�(j铆)鏁�(sh霉)鍜屽嚱鏁�(sh霉)鐨勬眰娉�.

5銆佸璁婇噺寰垎瀛�(xu茅)鍜屽弮璁婇噺绌嶅垎

鑰冭│鍏�(n猫i)瀹�

鈶� 鍙井鐨勫畾缇�锛� 鈶� 姹傚京(f霉)鍚堝嚱鏁�(sh霉)浠ュ強闅卞嚱鏁�(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)锛� 鈶�  澶氬厓鍑芥暩(sh霉)妤靛€肩悊璜栵紱 鈶� 鍙冭畩閲忕⿳鍒嗙殑涓€鑷存敹鏂傛€у垽鍒�锛� 鈶�  鍙冭畩閲忕⿳鍒嗙殑瑷�(j矛)绠楋紱 鈶� 鍙冭畩閲忕⿳鍒嗕竴鑷存敹鏂傛€ц唱(zh矛)鐨勯亱(y霉n)鐢ㄧ瓑.

鑰冭│瑕侀粸(di菐n)

锛�1锛夋帉鎻″鍏冨嚱鏁�(sh霉)鍙井鐨勫畾缇�锛岃兘鐔熺反鍒╃敤瀹氱京璀夋槑鏌愪簺甯歌(gu墨)鍑芥暩(sh霉)鐨勫彲寰€�锛屾帉鎻″鍏冨嚱鏁�(sh霉)鍙井銆侀€ｇ簩(x霉)銆佸彲姹傚亸灏�(d菐o)涔嬮枔鐨勯棞(gu膩n)绯�.

锛�2锛夌啛绶存帉鎻″鍏冨嚱鏁�(sh霉)寰�(f霉)鍚堝嚱鏁�(sh霉)姹傚亸灏�(d菐o)鏁�(sh霉)灏ゅ叾鏄珮闅庡亸灏�(d菐o)鏁�(sh霉)锛屾帉鎻℃柟绋嬫垨鏂圭▼绲勭⒑瀹氱殑闅卞嚱鏁�(sh霉)鍋忓皫(d菐o)鐨勮▓(j矛)绠�.

锛�3锛夌啛绶存帉鎻″鍏冨嚱鏁�(sh霉)妤靛€肩殑瑷�(j矛)绠�锛屽苟鑳借▓(j矛)绠楁湁鐣岄枆鍩熶笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬渶鍊�..

锛�4锛夌啛绶存帉鎻″惈鍙冭畩閲忓唬缇╃⿳鍒嗕竴鑷存敹鏂傛€х殑鍒ゅ垾.

锛�5锛夌啛绶存帉鎻″惈鍙冭畩閲忓父缇╃⿳鍒嗗拰寤ｇ京绌嶅垎鐨勮▓(j矛)绠�.

锛�6锛夌啛绶存帉鎻″惈鍙冭畩閲忓父缇╃⿳鍒嗗拰寤ｇ京绌嶅垎鐨勯€ｇ簩(x霉)鎬с€佸彲绌嶆€у拰鍙皫(d菐o)鎬�锛屽苟鑳藉埄鐢ㄩ€欎簺鎬ц唱(zh矛)閫�(j矛n)琛岃▓(j矛)绠楀拰璀夋槑..

6銆佸鍏冪⿳鍒嗗(xu茅)

鑰冭│鍏�(n猫i)瀹�

鈶犱簩閲嶇⿳鍒�銆佷笁閲嶇⿳鍒嗙殑瑷�(j矛)绠�锛� 鈶� 鏍兼灄鍏紡銆侀珮鏂叕寮忕殑闈堟椿閬�(y霉n)鐢�锛涒憿鍏╅鏇茬窔绌嶅垎銆佸叐椤炴洸闈㈢⿳鍒嗙殑瑷�(j矛)绠�锛涒懀 鍚勭ó绌嶅垎涔嬮枔鐨勭浉浜掗棞(gu膩n)绯荤瓑

鑰冭│瑕侀粸(di菐n)

锛�1锛夌啛绶存帉鎻′簩閲嶇⿳鍒嗐€佷笁閲嶇⿳鍒嗙殑瑷�(j矛)绠�锛岀啛绶存帉鎻￠檷缍�銆佹彌鍏冩硶锛屽挨鍏舵槸妤靛潗妯�(bi膩o)銆佺悆鍧愭(bi膩o)璁婃彌.

锛�2锛夌啛绶存帉鎻ree鍏紡銆丟auss鍏紡鐨勬浠跺拰绲�(ji茅)璜�.

锛�3锛夌啛绶存帉鎻＄涓€椤炲拰绗簩椤炴洸绶氱⿳鍒嗗拰鏇查潰绌嶅垎鐨勮▓(j矛)绠�.

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[1]     寰�(f霉)鏃﹀ぇ瀛�(xu茅)鏁�(sh霉)瀛�(xu茅)绯荤法. 鏁�(sh霉)瀛�(xu茅)鍒嗘瀽. 楂樼瓑鏁欒偛鍑虹増绀�, 1979

[2]     鑿澅甯寖澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯荤法.  鏁�(sh霉)瀛�(xu茅)鍒嗘瀽 楂樼瓑鏁欒偛鍑虹増绀�, 2001

[3] 寮靛(xu茅)杌�銆佺帇浠欐绛夌法. 鏁�(sh霉)瀛�(xu茅)鍒嗘瀽閬歌瑳. 婀栧崡甯寖澶у(xu茅)鍑虹増绀�锛�2012