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1、《计算方法》实验报告专业及班级:姓名：学号：日期：2013年6月12日一，方程求根1.用牛顿迭代法求解下列方程的正根（1）log(1+x)-x^2=0x=7.468818e-001求解代码：牛顿迭代法的函数M文件：functionx=Newt_n(f_name,x0)x=x0;xb=x+1;k=0;n=50;del_x=0.01;whileabs(x-xb)>0.000001k=k+1;xb=x;ifk>=nbreak;end;y=feval(f_name,x);y_driv=(feval(f_name,x+del_x)-y)/del_x;x=xb-y/y_driv;fp
2、rintf('k=%3.0f,x=%12.5e,y=%12.5e,yd=%12.5e',k,x,y,y_driv);end;fprintf('Finalanswer=%12.6e',x);待求方程的函数M文件：functiony=eqn_1(x)y=log(x+1)-x^2;运行结果：Newt_n('eqn_1',1)k=1,x=7.96954e-001,y=-3.06853e-001,yd=-1.51125e+000k=2,x=7.50200e-001,y=-4.90424e-002,yd=-1.04895e+000k=3,x=7.46936e-001,y=
3、-3.07003e-003,yd=-9.40663e-001k=4,x=7.46882e-001,y=-5.03365e-005,yd=-9.33074e-001k=5,x=7.46882e-001,y=-6.30906e-007,yd=-9.32949e-001Finalanswer=7.468818e-001（2）e^x-5x=0x=6.052671e-001待解方程：functiony=eqn_1(x)14y=exp(x)-5*x^2;运行结果：Newt_n('eqn_2',2)k=1,x=1.00102e+000,y=-1.26109e+001,yd=-1.262
4、39e+001k=2,x=6.88531e-001,y=-2.28918e+000,yd=-7.32552e+000k=3,x=6.11607e-001,y=-3.79584e-001,yd=-4.93453e+000k=4,x=6.05365e-001,y=-2.69226e-002,yd=-4.31343e+000k=5,x=6.05268e-001,y=-4.13312e-004,yd=-4.26254e+000k=6,x=6.05267e-001,y=-3.99547e-006,yd=-4.26175e+000Finalanswer=6.052671e-001an
5、s=0.6053（3）x^3+2x-1=0x=4.533977e-001待解方程：functiony=eqn_1(x)y=x^3+2*x-1;运行结果：Newt_n('eqn_3',3)k=1,x=1.89997e+000,y=3.20000e+001,yd=2.90901e+001k=2,x=1.15047e+000,y=9.65861e+000,yd=1.28868e+001k=3,x=6.80277e-001,y=2.82368e+000,yd=6.00536e+000k=4,x=4.82154e-001,y=6.75369e-001,yd=3.40884e+000
6、k=5,x=4.53984e-001,y=7.63945e-002,yd=2.71198e+000k=6,x=4.53401e-001,y=1.53570e-003,yd=2.63202e+000k=7,x=4.53398e-001,y=8.46834e-006,yd=2.63042e+000k=8,x=4.53398e-001,y=4.41262e-008,yd=2.63041e+000Finalanswer=4.533977e-001ans=0.4534（4）(x+2)^0.5-x=0x=2.0000待解方程：functiony=eqn_1(x)y=(x+2)^0.5
7、-x;运行结果：Newt_n('eqn_4',1)k=1,x=2.02879e+000,y=7.32051e-001,yd=-7.11565e-001k=2,x=2.00002e+000,y=-2.16052e-002,yd=-7.51049e-001k=3,x=2.00000e+000,y=-1.72788e-005,yd=-7.50157e-001k=4,x=2.00000e+000,y=-3.60276e-009,yd=-7.50156e-001Finalanswer=2.000000e+000ans=2.0000141
