Ⅰ Gauss縐鍒唌atlab鐨勭▼搴
% 楂樻柉-鍕掕╁痙鏁板肩Н鍒
fun=@(x)sin(x).*x.^3; % fun錛氱Н鍒琛ㄨ揪寮
% a,b錛氱Н鍒嗕笂涓嬮檺
a = 0;
b = pi;
tol=1e-8; % tol錛氱Н鍒嗙簿搴︼紝榛樿1e-6
% 璁＄畻奼傜Н鑺傜偣
syms x
p=sym2poly(diff((x^2-1)^(n+1),n+1))/(2^n*factorial(n));
tk=roots(p); % 奼傜Н鑺傜偣
% 璁＄畻奼傜Н緋繪暟
Ak=zeros(n+1,1);
for i=1:n+1
xkt=tk;
xkt(i)=[];
pn=poly(xkt);
fp=@(x)polyval(pn,x)/polyval(pn,tk(i));
Ak(i)=quadl(fp,-1,1,tol); % 奼傜Н緋繪暟
end
% 縐鍒嗗彉閲忎唬鎹錛屽皢[a,b]鍙樻崲鍒癧-1,1]
xk=(b-a)/2*tk+(b+a)/2;
% 媯楠岀Н鍒嗗嚱鏁癴un鏈夋晥鎬
fun=fcnchk(fun,'vectorize');
% 璁＄畻鍙橀噺浠ｆ崲涔嬪悗縐鍒嗗嚱鏁扮殑鍊
fx=fun(xk)*(b-a)/2;
% 璁＄畻縐鍒嗗
ql=sum(Ak.*fx)
quadl(fun,0,pi) % 璋冪敤MATLAB鍐呴儴縐鍒嗗嚱鏁版楠
Ⅱ 奼傚姪錛孧atlab楂樻柉鍕掕╁痙奼傚嶆潅縐鍒
楂樻柉涓鍕掕╁痙奼傜Н鍏寮忚緝澶嶆潅,涓嶉傚悎涓鑸璁＄畻搴旂敤銆傛枃鐚甗3]鎻愪緵浜嗗彉姝ラ暱楂樻柉涓鍕掕╁痙縐鍒嗙畻娉,鍏跺熀鏈鎬濇兂鏄鍩轟簬澶嶅寲奼傜Н鐨勬濇兂,瀵逛簬杈冮暱鍖洪棿[a,b銆,閫氳繃涓嶆柇鍦頒簩鍒嗗尯闂,姣
Ⅲ matlab瀵歸珮鏂鍑芥暟奼傜Н鍒嗭紝縐鍒嗕笅闄愭槸璐熸棤絀鳳紝涓婇檺鏄痻錛寈鍙栧兼槸浠-255錛255鐨勬暟緇勶紝瑕佹庝箞寮勶紵
搴旇ョ敤璇宸鍑芥暟erf鏉ユ眰銆
1銆侀栧厛錛岀Н鍒嗕笂涓嬮檺錛
鈭(-鈭,x)搴斿垎鎴愨埆(-鈭,0)+鈭(0,x)=-鈭(0,-鈭)+鈭(0,x)
2銆佽縐鍙橀噺t搴斾綔鍙樻崲錛
t1=t/蟽 鈫 t=蟽*t1
鐩稿簲鐨勭Н鍒嗛檺x鍙樹負x/蟽
3銆佺郴鏁幫細
dt=蟽*dt1錛屜冨拰鍘熺郴鏁板垎姣嶄腑鐨勏冪害鍒嗭紝浣欎笅1/鈭(2蟺)錛屼笌erf鍑芥暟鐨勭郴鏁板圭収錛屽簲璇ヤ箻浠1/(2鈭2)
緇間笂錛屽師琛ㄨ揪寮忕殑璁＄畻濡備笅錛埾冪殑鍙栧艱嚜瀹氾級錛
x=-255:255;
sigma=100;
f=1/(2*(2)^0.5) * ( erf(x/sigma)-erf(-inf) )