数值分析1.2.doc

数值分析(供参考)(注：所有matlab代码采用横宽字体)1. 求方程 x3-x2-1在x0=1.5附近的根. fun=inline(x2+1)(1/3); x=1.5; k=1; while abs(x-fun(x)1e-5&k=500 x=fun(x); k=k+1; end x x =1.46562.求x3-3x-1=0在x0=2附近的根. 解： 迭代公式为：xk+1=(xk-xk3-3xk-13xk2-3） x=2;k=1;fun=inline(x-(x3-3*x-1)/(3*x2-3); while abs(x-fun(x)1e-5&k=500 x=fun(x); k=k+1; end xx =1.87943.求 x-tanx=0的最小正根.xk+1=(xk-tanxk)/(1-1cos2xk)fun=inline(x-(x-tan(x)/(1-1/(cos(x)2); x=4.5;k=1;while abs(fun(x)-x)1e-5&k=500 x=fun(x); k=k+1; end xx = 4.49344.求x2-3x+2-ex=0的根.解：迭代公式为xk+1=(xk-xk2-3xk+2-exk2xk-3-exk） x=0:0.1:5; y=x.2-3*x+2-exp(x); plot(x,y) axis(0 5 -5 5) grid onfun=inline(x-(x.2-3*x+2-exp(x)/(2*x-3-exp(x); x=1;k=1;while abs(fun(x)-x)1e-5&k=500 x=fun(x); k=k+1; end xx = 0.25755.已知实验数据如下：xi1925313844yi19.032.349.073.397.8用最小二乘法求形如y=a+bx2的经验公式，并计算均方误差. x=19 25 31 38 44; y=19.0 32.3 49.0 73.3 97.8; z=x.2; p=polyfit(z,y,1)p = 0.0500 0.9726sigma=sqrt(sum(p(1)*z(1:5)+p(2)-y(1:5).2)/5)sigma = 0.0548a=0.9726 ; b=0.5000;均方误差=0.0548.6.已知xi0.20.40.60.81.0yi0.980.920.810.640.38求4次牛顿插值多项式x=0.2 0.4 0.6 0.8 1.0; y=0.98 0.92 0.81 0.64 0.38; f=y; for i=1:4; for j=i+1:5; f(j)=(f(j)-f(i)/(x(j)-x(i); end end ff =0.9800 -0.3000 -0.6250 -0.2083 -0.5208故N4x=0.9800+-0.3000x-0.2+-0.6250x-0.2x-0.4+-0.2083x-0.2x-0.4x-0.6+(-0.5208)x-0.2x-0.4x-0.6(x-0.8)6.求解初值问题 dydx=1x2-yx, x1,2,y1=1.解：(1) 创建函数文件funt.m，FileNewM-File,输入：function f=odefun(x,y)f=1/(x.2)-y/x;保存为odefunt.m(2)在命令窗口(Command Window)中输入：x=1:0.1:2; x,y=ode45(odefun,x,1); plot(x,y) yans = 1.0000 0.9957 0.9853 0.9710 0.9546 0.9370 0.9188 0.9004 0.8821 0.8641 0.84667.求解初值问题 dydx=-50y+50x2+2x, x0,1,y0=13.解：(1) 创建函数文件funt2.m，FileNewM-File,输入：function f=odefun2(x,y)f=-50*y+50*x.2+2*x;保存为odefunt2.m(2)在命令窗口(Command Window)中输入：x=0:0.1:1; x,y=ode45(odefun2,x,1/3); plot(x,y) yans = 0.3333 0.0122 0.0400 0.0900 0.1600 0.2501 0.3600 0.4899 0.6399 0.8099 1.00028.画出y=sin(tanx