瀹為獙鎶ュ憡涓�
棰樼洰
锛?/p>
闈炵嚎鎬ф柟绋嬫眰瑙?/p>
鎽樿
锛氶潪绾挎�ф柟绋嬬殑瑙ｆ瀽瑙ｉ�氬父寰堥毦缁欏嚭锛?/p>
鍥犳绾挎�ф柟绋嬬殑鏁板�艰В娉曞氨灏や负閲嶈銆?/p>
鏈疄楠岄噰鐢?/p>
涓ょ甯歌鐨勬眰瑙ｆ柟娉曚簩鍒嗘硶鍜?/p>
Newton
娉曞強鏀硅繘鐨?/p>
Newton
娉曘�?/p>
鍓嶈█锛?/p>
锛堢洰鐨勫拰鎰忎箟锛?/p>
鎺屾彙浜屽垎娉曚笌
Newton
娉曠殑鍩烘湰鍘熺悊鍜屽簲鐢ㄣ�?/p>
鏁板鍘熺悊
锛?/p>
瀵逛簬涓�涓潪绾挎�ф柟绋嬬殑鏁板�艰В娉曞緢澶氥�?/p>
鍦ㄦ浠嬬粛涓ょ鏈�甯歌鐨勬柟娉曪細
浜屽垎娉曞拰
Newton
娉曘�?/p>
瀵逛簬浜屽垎娉曪紝
鍏舵暟瀛﹀疄璐ㄥ氨鏄瀵逛簬缁欏畾鐨勫緟姹傝В鐨勬柟绋?/p>
f(x)
锛?/p>
鍏跺湪
[
a,b
]
涓婅繛缁紝
f(a)f(b)<0
锛?/p>
涓?/p>
f(x)
鍦?/p>
[
a,b
]
鍐呬粎鏈変竴涓疄鏍?/p>
x
*
锛屽彇鍖洪棿涓偣
c
锛岃嫢锛屽垯
c
鎭颁负鍏舵牴锛屽惁鍒欐牴鎹?/p>
f(a)f(c)<0
鏄惁
鎴愮珛鍒ゆ柇鏍瑰湪鍖洪棿
[
a,c
]
鍜?/p>
[
c,b
]
涓殑鍝竴涓紝浠庤�屽緱鍑烘柊鍖洪棿锛屼粛绉颁负
[
a,b
]
銆傞噸澶嶈繍琛岃绠楋紝鐩?/p>
鑷虫弧瓒崇簿搴︿负姝€�傝繖灏辨槸浜屽垎娉曠殑璁＄畻鎬濇兂銆?/p>
Newton
娉曢�氬父棰勫厛瑕佺粰鍑轰竴涓寽娴嬪垵鍊?/p>
x
0
锛岀劧鍚庢牴鎹叾杩唬鍏紡
浜х敓閫艰繎瑙?/p>
x
*
鐨勮凯浠ｆ暟鍒?/p>
{
x
k
}
锛岃繖灏辨槸
Newton
娉曠殑鎬濇兂銆傚綋
x
0
鎺ヨ繎
x
*
鏃舵敹鏁涘緢蹇紝浣嗘槸褰?/p>
x
0
閫夋嫨涓嶅ソ鏃讹紝鍙兘浼氬彂鏁ｏ紝鍥犳鍒濆�肩殑閫夊彇寰堥噸瑕併�傚彟澶栵紝鑻ュ皢璇ヨ凯浠ｅ叕寮忔敼杩涗负
鍏朵腑
r
涓鸿姹傜殑鏂圭▼鐨勬牴鐨勯噸鏁帮紝杩欏氨鏄敼杩涚殑
Newton
娉曪紝褰撴眰瑙ｅ凡鐭ラ噸鏁扮殑鏂圭▼鐨勬牴鏃讹紝
鍦ㄥ悓绉嶆潯浠朵笅鍏舵敹鏁涢�熷害瑕佹瘮
Newton
娉曞揩鐨勫銆?/p>
绋嬪簭璁捐
锛?/p>
鏈疄楠岄噰鐢?/p>
Matlab
鐨?/p>
M
鏂囦欢缂栧啓銆傚叾涓緟姹傝В鐨勬柟绋嬪啓鎴?/p>
function
鐨勬柟寮忥紝濡備笅
function y=f(x);
y=-x*x-sin(x);
鍐欐垚濡備笂褰㈠紡鍗冲彲锛屼笅闈㈢粰鍑轰富绋嬪簭銆?/p>
浜屽垎娉曟簮绋嬪簭锛?/p>
clear
%%%
缁欏畾姹傝В鍖洪棿
b=1.5;
a=0;