加步探索法
#include<iostream>
#include<math.h>
using namespace std;
double fun(double t)
{
return (t*t*t-2*t+1);
}
double max(double a,double b)
{
if(a>b)return a;
else return b;
}
double min(double a,double b)
{
if(a>b)return b;
else return a;
}
double Addstep(double(*pfun)(double t))
{
int k=0;
double t0=0,h=1,r=2,t,a=0,b=0;
t=t0+h;
do{
if(fun(t)<fun(t0)){h=r*h;t0=t;t=t0+h;k++;}
else{if(k=0){h=-h;k++;}
else{a=min(t0,t);b=max(t0,t);return a;return b;}}
}while(a=b);
cout<<" 探索区间为："<<"["<<min(t0,t)<<","<<max(t0,t)<<"]"<<endl; }
int main()
{
Addstep(fun);
return 0;
}
对分法
#include<iostream>
#include<math.h>
using namespace std;
double fun(double t)
{
return (t*t-3*t);
}
double dfun(double t)
{
return (2*t-3);
}
void Dichotomous(double(*pfun)(double t),double (*pdfun)(double t)) {
int maxflag=1000,k=1;
double a=-3,b=5,c,err=0.1,t;
do
{
c=(a+b)/2;
if(dfun(c)<0){a=c;}
else {if(dfun(c)>0){b=c;}
else{a=c;b=c;}}
k++;
}while(fabs(a-b)>err&&k<maxflag);
if(k>=maxflag)
cout<<endl<<"对分法迭代失败!迭代次数为k="<<k<<endl;
else
{
cout<<endl<<" 对分法迭代成功!迭代次数为k="<<k-1<<endl; cout<<"迭代结果：近似根为root="<<t<<endl;
cout<<" 函数值近似为：f(root)="<<fun(t)<<endl;
}
}
int main()
{
Dichotomous(fun,dfun);
return 0;
}
Newton切线法
#include<iostream>
#include<math.h>
using namespace std;
double fun(double t)
{
return (t*t*t-2*t+1);
}
double dfun(double t)
{
return (3*t*t-2);
}
void NewtonIterative(double(*pfun)(double t),double (*pdfun)(double t)) {
int maxflag=1000,k=1;
double t0=1,err=0.01,t;
do
{
t0=t;
t=t0-pfun(t0)/pdfun(t0);
k++;
}while(fabs(t-t0)>err&&k<maxflag);
if(k>=maxflag)
cout<<endl<<" 牛顿迭代失败!迭代次数为k="<<k<<endl;
else
{
cout<<endl<<" 牛顿迭代成功!迭代次数为k="<<k-1<<endl;
cout<<" 迭代结果：近似根为root="<<t<<endl;
cout<<" 函数值近似为：f(root)="<<fun(t)<<endl;
}
}
int main()
{
NewtonIterative(fun,dfun);
return 0;
}
黄金分割法
#include<iostream>
#include<math.h>
using namespace std;
double fun(double t)
{
return (t*t+2*t);
}
void Goldensection(double(*pfun)(double t))
{
int maxflag=1000,k=1;
double a=-3,b=5,err=0.001,t,t1,t2;
do
{
t1=a+0.618*(b-a);
t2=b-0.618*(b-a);
if(t1=t2){a=t2;b=t1;}
else {if(t1<t2){a=t2;}
else{b=t1;}}
k++;
}while(fabs(a-b)>err&&k<maxflag);
if(k>=maxflag)
cout<<endl<<"黄金分割法迭代失败!迭代次数为k="<<k<<endl; else
{
t=(a+b)/2;
cout<<endl<<" 黄金分割法迭代成功!迭代次数为k="<<k-1<<endl;
cout<<" 迭代结果：近似根为root="<<t<<endl; cout<<" 函数值近似为：f(root)="<<fun(t)<<endl; }
}
int main()
{
Goldensection(fun);
return 0;
}
抛物线插值法
#include<iostream>
#include<math.h>
using namespace std;
double fun(double x)
{
return (8*x*x*x-2*x*x-7*x+3);
}
double max(double a,double b)
{
if(a>b)return a;
else return b;
}
double min(double a,double b)
{
if(a>b)return b;
else return a;
}
void Parainterpolation(double(*pfun)(double x)) {
double a=0,b=2,err=0.001,x=0,x0=1,f,f0;
do
{
x=((x0*x0-b*b)*fun(a)+(b*b-a*a)*fun(x0)+(a*a-x0*x0)*fun(b))/(2*((x0-b)*fun(a)+(b-a)*fun(x0) +(a-x0)*fun(b)));
f0=fun(x0);
f=fun(x);
if(f=f0){a=min(x,x0);b=max(x,x0);x0=(a+b)/2;}
else {
if((fun(x)-f0)*(x-x0)>0)
{
b=max(x,x0);x0=min(x,x0);
}
else
{
a=min(x,x0);x0=max(x,x0);
}
}
}while(fabs(x-x0)>err);
x=(x+x0)/2;
cout<<" 迭代结果：近似根为root="<<x<<endl;
cout<<" 函数值近似为：f(root)="<<fun(x)<<endl;
}
int main()
{
Parainterpolation(fun);
return 0;
}。