matlab编程实现二分法,牛顿法,黄金分割法,最速下降matlab程序代码

1、用二分法求解mm/()t4-2t2-4tt,1，15内的极小值点，要求准1.functiontd=erfenfa(a,b)k=1;%记录循环次数whileabs(a-b)0.0005c=(a+b)/2;C(k)=c;%存储每次循环中点c的值ifff(c)0b=c;endk=k+1;endt=(a+b)/2;%最终符合要求的值d=f(t);%最优解Ckfunctiony=f(t)y=t4-2*t2-4*t;functiony=ff(t)y=4*t3-4*t-4;运行结果td=erfenfa(1,1.5)C=Columns1through91.25001.37501.31251.34381.328

2、11.32031.32421.32621.3252Column101.3247111.3250d=收敛精度0.5-5.72902.黄金分割法f(x)=x3-2x+1初始区间0,3functiont,f=huangjinfenge(a,b)m=1-(sqrt(5)-1)/2;t2=a+m*(b-a)f2=g(t2);t1=a+b-t2f1=g(t1);whileabs(t1-t2)0.5iff1t,f=huangjinfenge(0,3)t2=1.1459t1=1.8541t1=1.1459t2=0.7082t=0.9271f=-0.05743.用牛顿法求解minf(兀)9兀2sin兀1初始迭代

3、点为兀0=04,要求准确到小数点后第5位小数functiont1,d=Newton(t0)t=t0-ff(t0)/fff(t0);k=l;%记录迭代次数T(l)=t;%存储迭代点whileabs(t-t0)0.000005t0=t;t=t0-ff(t)/fff(t);k=k+1;T(k)=t;endt1=t0;d=f(t1);kTfunctiony=f(x)y=9*x2-sin(x)-l;functiony=ff(x)y=18*x-cos(x);functiony=fff(x)y=18+sin(x);运行结果t1,d=Newton(0.4)T=0.05860.05550.0555t1=0.05

4、55d=-1.02774.最速下降法验证课本上的例题求解minf(兀)9兀2-sin兀-1初始迭代点为x0=0.4,要求准确到小数点后第5位小数functionG,g,X,F=zuisu(X0)F(l)=f(XO);%存储x点处的值G(:,1)=h(X0);%存储梯度向量g(l)=norm(G(:,l);%存储梯度模长X(:,1)=XO;%存储x值A=2,0;0,8;forj=1:2X(:,j+1)=X(:,j)-(G(:,j)*G(:,j)/(G(:,j)*A*G(:,j)*G(:,j);F(j+1)=f(X(:,j+1);G(:,j+1)=h(X(:,j+1);g(j+1)=norm(G(:,j+1);endif(G(:,2)*G(:,1)1E-10&G(:,3)*G(:,2)G,g,X,F=zuisu(X0)相邻两搜索方向是正交的G=0.22150.88622.00001.47698.0000-0.3692g=8.24621.