Numerical-Analysis Homework

1.Newton iteration

python

def f(x):
    return 6*x**5-5*x**4-4*x**3+3*x**2

def df(x):
    return 30*x**4-20*x**3-12*x**2+6*x

def dx(f, x):
    return abs(0-f(x))

def newtons_method(f, df, x0, e):
    delta = dx(f, x0)
    while delta > e:
        x0 = x0 - f(x0)/df(x0)
        delta = dx(f, x0)
    print('Root is at: ', x0)
    print('f(x) at root is: ', f(x0))

x0s = [0, .5, 1]
for x0 in x0s:
    newtons_method(f, df, x0, 1e-5)

2.Power method

cpp

#include 
#include 
#define N 3
void matrixx(double A[N][N],double x[N],double v[N])
{
    for(int i=0; iv[i+1]?v[i]:v[i+1];
    return max;
}
void main()
{
//data input
    double A[N][N]= {2,-1,0,0,2,-1,0,-1,2};
    double x[N]= {0,0,1};
    double v[N]= {0,0,0};
    double u[N]= {0,0,0};
    double p[N]= {0,0,0};
    double e=1e-10,delta=1;
    int k=0;
    while(delta>=e)
    {
        for(int q=0; q

3.Gauss-Seidel iteration

cpp

#include "stdio.h"
#include "stdlib.h"
#include "math.h"


#define N 3
#define MAXITER 10000


void main()
{
    int i, j, k;
    int iter = 0;
    int count;
//系数矩阵
    double a[N][N] = {10, -1, -2, -1, 10, -2, -1, -1, 5};
//方程右边的值
    double b[N] = {72, 83, 42};
    double new_x[N] = {0};
    double old_x[N] = {0};
    double e = 0.0000001;
    bool flag = false;
//开始迭代
    while(itere)
            {
                count++;
                break;
            }
        if(count==0)
            flag = true;
    }
    for(i=0; i