數(shù)學(xué)Matlab實驗

1、實驗項目 ： matlab 基本實驗二、實驗?zāi)康暮鸵骯. 熟悉 matlab 軟件的用戶環(huán)境， 掌握其一般目的命令和 matlab 數(shù)組操作與 運(yùn)算函數(shù)；b. 掌握 matlab 軟件的繪圖命令，能夠熟練應(yīng)用循環(huán)和選擇結(jié)構(gòu)實現(xiàn)各種循環(huán) 選擇功能；c. 借助 matlab 軟件的繪圖功能，對函數(shù)的特性進(jìn)行探討，廣泛聯(lián)想，大膽猜 想，發(fā)現(xiàn)進(jìn)而證實其中的規(guī)律。三、實驗內(nèi)容將方程 x5+5x3-2 x+1=0 改寫成各種等價的形式進(jìn)行迭代，觀察迭代是否收斂，并給出解釋。x1=-2:0.01:2;x2=-3:0.01:3;x3=-4:0.01:4;x4=-5:0.01:5;y1=x1.a5 +5*xm

2、*x1+1;y2=x245 +5*x2.a3-2*x2+1;y3=x3.a5 +5*x3.a3-2*x3+1;y4=x4.a5 +5*x4.a3-2*x4+1;subplot(2,2,1),plot(x1,y1),title( ' 子圖 (1)' ) ,grid on, subplot(2,2,2),plot(x2,y2),title(' 子圖 (2)'),gridon,subplot(2,2,3),plot(x3,y3),title(' 子圖 (3)'),gridon,subplot(2,2,4),plot(x4,y4),title( '

3、; 子圖 (4)' ) ,grid on,第 1頁 / 共 16 頁子圖子圖子圖子圖子圖子圖子圖子圖由圖可知 x的初值應(yīng)在(-0.78 , 0.76)之間。(2)解：第一步 構(gòu)造迭代函數(shù)x = f ( x)53x 5x 1x = x = f_,(x)21 3 2 1xx2 x = f2 (x)5 5x 5 x521x = .盲-右x = f3(x)x xx第二步利用加速迭代收斂法變形后：53-4x - 10 x 亠 1x4廠 x 二 f1(x)2 5 x -15 x6 22x -4x 3xx = f2 (x)x355x 3x2x -222x +8xx 二 f3(x)x - 53x55

4、x36 x -1第三步迭代設(shè)定初值第2頁/共16頁x。= -0.75xn ! = f (xn) n=0,1,2,3用matlab編程 x=-077;y=-0.77;z=-0.77;for k=1:30x=(-4*xa5-10*xa3+1)/(2-5*xa4-15*xa2);y=(2*ya6+4*ya2-3*y)/(5*ya3+3*ya5+2*y-2);z=(8*za2-2*z)/(za5+5*za3+6*z-1);x,y, z;end迭代結(jié)果為：x =-61.5948 y =-0.7685 x =-49.2694 y =-0.7685 x =-39.4074 y =-0.7685-31.515

5、8第3頁/共16頁-0.7685 x =-25.2000 y =-0.7685 x =-20.1442 y =-0.7685 x =-16.0957 y =-0.7685 x =-12.8521 y =-0.7685第 #頁 / 共 16 頁-10.2512 y =-0.7685 x =-8.1634 y =-0.7685 x =-6.4844 y =-0.7685 x =-5.1311 y =-0.7685 x =-4.0373-0.7685 x =-3.1508 y =-0.7685 x =-2.4323 y =-0.7685 x =-1.8546 y =-0.7685 x =-1.402

6、8 y =-0.7685x =第 #頁 / 共 16 頁-1.0737 y =-0.7685 x =-0.8700 y =-0.7685 x =-0.7840 y =-0.7685 x =-0.7689 y =-0.7685 x =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685-0.7685x =第 #頁 / 共 16 頁-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =

7、-0.7685 x =-61.5948 y =-49.2694 y =-0.7685 x =-39.4074 y =-0.7685 x =-31.5158 y =-0.7685 x =-25.2000 y =-0.7685 x =-20.1442第 # 頁 / 共 16 頁-0.7685 x =-16.0957 y =-0.7685 x =-12.8521 y =-0.7685 x =-10.2512 y =-0.7685 x =-8.1634 y =-6.4844 y =-0.7685 x =-5.1311 y =-0.7685 x =-4.0373 y =-0.7685 x =-3.1508 y =-0.7685 x =-2.4323第 # 頁 / 共 16 頁-0.7685 x =-1.8546 y =-0.7685 x =-1.4028 y =-0.7685 x =-1.0737 y =-0.7685 x =-0.8700 y =-0.7685-0.7840-0.7685 x =-0.7689 y =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685第 # 頁 / 共 16 頁-0.7685 y =-0.7685 x =-