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1、出解释1、将方程x5 +5x3-2x + 1 = 0改写成各种等价的形式进行迭代，观察迭代是否收敛，并给(1)画图：x1=-6:0.01:6;x2=-3:0.01:3;x3=-1:0.01:1;x4=-0.8:0.01:-0.75;y1=x1. A5 +5*x1. A3-2*x1 + 1;y2=x2. A5 +5*x2.A3-2*x2+1;y3=x345 +5*x3.A3-2*x3+1; y4=x4.A5 +5*x4.A3-2*x4+1; subplot(2,2,1),plot(x1,y1) ,title(子图(1) ,gridon, subplot(2,2,2),plot(x2,y2) ,t
2、itle( 子图(2),grid onsubplot(2,2,3),plot(x3,y3) ,title( 子图(3),grid on, subplot(2,2,4),plot(x4,y4) ,title( 子图(4) ,grid on,10.50-05-1-10-505104D0子图(2); ：/200,.一 一一一 一, 1MliM.SMMH1IBiJri)jfaf0p-200Jr,if. jii-400if,114024由图可知x的初值应在(-0.78 , 0.76 )之间(2)解：第一步构造迭代函数x5 5x3X = fi(x)x = f 2(x)x = f3(x)1321x 25 5
3、x 5x521第二+3 -2利用加速送x收敛法变形后-4x5 -10x 3 142 x 二 f 1(x)2 5x -15xx 二 f2(x)X = f3(x)2x -4x2 -3x355x 3x 2x-2-2x+8x 2X . 53x +5x +6x 1第三步迭代iXQW.75x 1 二 f g n=0,1,2,3 用MATLAB编程x=-077;y=-0.77;z=-0.77;for k=1:30x=(-4*x A5-10*x A3+1)/(2-5*x A4-15*x A2);y=(2*y A6+4*y A2-3*y)/(5*y A3+3*y A5+2*y-2);z=(8*zA2-2*z)/
4、(zA5+5*zA3+6*z-1);x,y, z;end迭代结果为：x =-61.5948-49.2694 y =- 0.7685 x =-39.4074 y =- 0.7685 x =-31.5158 y =- 0.7685 x =-25.2000 y =-0.7685-20.1442- 0.7685 x =-16.0957 y =- 0.7685 x =-12.8521 y =- 0.7685 x =-10.2512 y =-0.7685 x =-8.1634-6.4844 y =-0.7685 x =-4.0373 y =-0.7685 x =-3.1508 y =-0.7685- 0.7685 x =- 1.8546 y =- 0.7685 x =- 1.4028 y =- 0.7685 x =- 1.0737 y =- 0.7685 x =- 0.7685 x =- 0.7840 y =- 0.7685 x =- 0.7689 y =- 0.7685 x =- 0.7685 y =- 0.7685 x =-0.7685- 0.7685 y =- 0.7685 x =- 0.7685 y =-0.7685 x =-0.7685 x =-0.7685 y =-0.7685-0.7685 x =-0.7685 y =-0.7685 x =-0.7685 y =-0.7685
