方程求根计算器实验报告一C++版

1、计算方法实验题目：班级：学号：姓名：19计算方法与实习实验报告目录计算方法实验11 实验目的32 实验步骤32.1环境配置：32.2添加头文件32.3主要模块33 代码43.1主程序部分43.2多项式方程部分43.3核心算法部分73.4数据结构部分114运行结果164.1二分法运行结果164.2牛顿迭代法运行结果174.3割线法运行结果18边界情况调试185总结20输入输出20二分法20牛顿迭代法20割线法206参考资料201 实验目的1. 通过编程加深二分法、牛顿法和割线法求解多项式方程的理解2. 观察上述三种方法的计算稳定性和求解精度并比较各种方法利弊2 实验步骤2.1环境配置：VS201

2、3，C+控制台程序2.2添加头文件#include "stdio.h"#include "stdlib.h"#include "stdafx.h"2.3主要模块程序一共分成三层，最底层是数据结构部分，负责存储数据，第二层是交互部分，即多项式方程部分，负责输入输出获得数据，最上层是核心的算法部分，负责处理已获得的数据。主函数负责获取方程系数并显示，算法和方程作为后台程序，顺序表作为存储手段。3 代码3.1主程序部分/ squencelistandlinklist1.cpp : 定义控制台应用程序的入口点。/#include "

3、stdio.h"#include "stdlib.h"#include "stdafx.h"#include "squencelist.h"#include "equation.h"#include<iostream>/主程序/int _tmain(int argc, _TCHAR* argv)GetEquation();ShowMenu();return 0;3.2多项式方程部分l 方程部分头文件#ifndef _EQUATION_H#define _EQUATION_H#include &

4、quot;squencelist.h"#include "stdio.h"#include "stdlib.h"extern int highestx;extern sequenlist *B;extern sequenlist *D;double Function(sequenlist *B, double x);void GetEquation(void);void ShowMenu(void);void printfunction(sequenlist *A);sequenlist Derivative(sequenlist *A, in

5、t highestx);#endifl 方程部分CPP文件#include "stdafx.h"#include "equation.h"#include "math.h"#include "algorithm.h"#include "squencelist.h"/全局变量int highestx=0;sequenlist *B;sequenlist *D;/多项式函数/double Function(sequenlist *A,double x)double f = 0.00;int i;fo

6、r (i = 1; i <= A->last; i+)f = f + A->datai * pow(x, A->last - i);return f;/多项式函数系数/void GetEquation(void)int j = 0;int x = 0;B = InitList();cout << "方程最高项次数（如y=x3最高项次数为3）：" << endl;cin >> highestx;cout << "输入方程系数,输入00结束（如y=x2+2x+1输入1 2 1 00）:"

7、 << endl;cin >> x;while (x != 00)for (j = 1; j <= highestx + 1; j+)if (!Insert(B, x, j)exit(0);cin >> x;j = 1;printfunction(B);/显示交互/void ShowMenu(void)int x;double a, b, ex, ef, res, x0,x1;cout << "选择求解方程根的方法：" << endl;cout << "1.二分法求解" <

8、;< endl;cout << "2.牛顿迭代法求解" << endl;cout << "3.割线法求解" << endl;cin >> x;switch (x)case 1:cout << "请输入区间上下限（如【a,b】输入a b）：" << endl;cin >> a >> b;cout << "请输入根的容许误差和函数的容许误差（若只有一个误差则另一项为0）：" << e

9、ndl;cin >> ex >> ef;res = Dichotomy(a,b,ex,ef);break;case 2:cout << "请输入初始值x0：" << endl;cin >> x0;cout << "请输入根的容许误差和函数的容许误差（若只有一个误差则另一项为0）：" << endl;cin >> ex >> ef;res = Newtonsmethod(x0, ex, ef);break;case 3:cout << &

10、quot;请输入初始值x0,x1：" << endl;cin >> x0 >> x1;cout << "请输入根的容许误差和函数的容许误差（若只有一个误差则另一项为0）：" << endl;cin >> ex >> ef;res = Cutmethod(x0, x1, ex, ef);break;default:break;/打印输出函数/void printfunction(sequenlist *A)int i;cout << "f="for (

11、i = 1; i < A->last; i+)if (A->datai+1 < 0)cout << A->datai << "*" << "x" << A->last - i;else cout << A->datai << "*" << "x" << A->last - i << "+"cout << A->datai &

12、lt;< endl;/函数微分/sequenlist Derivative(sequenlist *A, int highestx)int i;D = InitList();for (i = 1; i <= A->last; i+)Insert(D,( A->datai * (A->last - i), i);D->last = A->last - 1;return *D;3.3核心算法部分l 算法部分头文件#ifndef _ALGORITHM_H#define _ALGORITHM_H#include "stdio.h"#incl

13、ude "stdlib.h"int Judge(double x1, double x0, double e);double Dichotomy(double xa, double xb, double ex, double ef);double Newtonsmethod(double x0, double ex, double ef);double Cutmethod(double x1, double x0, double ex, double ef);#endifl 算法部分CPP文件#include "algorithm.h"#include

14、"stdafx.h"#include "squencelist.h"#include "equation.h"/误差判别/inline int Judge(double x1, double x0, double e)if (e = 0)return 0;if (x1 = 0)if (fabs(x0) < e)return 1;else return 0;if (x0 = 0)if (fabs(x1) < e)return 1;else return 0;if (fabs(x1 - x0) < e)return 1;

15、else return 0;/二分法/double Dichotomy(double xa, double xb, double ex, double ef)cout << "/二分法/" << endl;double xn = 0, fn = 0, fa = Function(B, xa), fb = Function(B, xb);double a, b;int n = 1, flag = 0;a = xa;b = xb;cout << "二分次数" << "t" <<

16、'x' << "tt" << "f(x)" << endl;if (fa*fb > 0)cout << "无法使用二分法" << endl;flag = 1;while (1)if (fa = 0)xn = xa;cout << n+ << "tt" << xn << "tt" << Function(B, xn) << endl;break;

17、if (fb = 0)xn = xb;cout << n+ << "tt" << xn << "tt" << Function(B, xn) << endl;break;xn = (a + b) / 2;fn = Function(B, xn);cout << n+ << "tt" << xn << "tt" << Function(B, xn) << endl;if (f

18、n = 0)break;if (fn*fa < 0)b = xn;flag = (Judge(a, b, ex) | Judge(fn, 0, ef);else if (fn*fb < 0)a = xn;flag = (Judge(a, b, ex) | Judge(fn, 0, ef);if (flag)break;return xn;/牛顿迭代法/double Newtonsmethod(double x0, double ex, double ef)double xn = 0, fn = 0, dfn = 0;int n = 1, flag = 0;cout <<

19、 "/牛顿迭代法/" << endl;cout << "迭代次数" << "t" << "x" << "tt" << "f(x)" << endl;*D = Derivative(B, highestx);fn = Function(B, x0);dfn = Function(D, x0);if (fabs(fn) < ef)flag = 1;while (1)if (dfn = 0)c

20、out << "导数为零" << endl;break;xn = x0 - fn / dfn;fn = Function(B, x0);dfn = Function(D, x0);flag = (Judge(xn, x0, ex) | Judge(fn, 0, ef);if (flag)break;x0 = xn;cout << n+ << "tt" << xn << "tt" << Function(B, xn) << endl;if (

21、n > 3000)cout << "迭代失败" << endl;return 0;return xn;/割线法/double Cutmethod(double x1, double x0, double ex, double ef)double xn, fn, f0, f1;int n = 1, flag = 0;cout << "/割线法/" << endl;cout << "迭代次数" << "t" << "x&

22、quot; << "tt" << "f(x)" << endl;*D = Derivative(B, highestx);f0 = Function(B, x0);f1 = Function(B, x1);if (fabs(f0) < ef)cout << n+ << "tt" << x0 << "tt" << Function(B, x0) << endl;return x0;if (fabs(f1)

23、 < ef)cout << n+ << "tt" << x1 << "tt" << Function(B, x1) << endl;return x1;if (Judge(x1, x0, ex)cout << n+ << "tt" << x1 << "tt" << Function(B, x1) << endl;return x1;while (!flag)xn =

24、x1 - f1*(x1 - x0) / (f1 - f0);fn = Function(B, xn);flag = (Judge(xn, x1, ex) | Judge(fn, 0, ef);cout << n+ << "tt" << xn << "tt" << Function(B, xn) << endl;x0 = x1;x1 = xn;if (n > 3000)cout << "迭代失败" << endl;return 0;re

25、turn xn;3.4数据结构部分l 数据结构头文件#ifndef _SQUENCELIST_H#define _SQUENCELIST_H#include "stdio.h"#include "stdlib.h"#include "stdafx.h"#include<iostream>using namespace std;#define maxsize 1024/*sequenlist*/typedef int datatype;typedef structdatatype datamaxsize;int last;s

26、equenlist;sequenlist *InitList();int Length(sequenlist*);int Insert(sequenlist*, datatype, int);int Delete(sequenlist*, int);int Locate(sequenlist*, datatype);void del_node(sequenlist*, datatype);void PrintList(sequenlist*);int Compare_L(sequenlist*, sequenlist*);void Invert(sequenlist*);/*linklist*

27、/typedef char linkdatatype;typedef struct nodelinkdatatype data;struct node*next;linklist;linklist* CreateListF();#endifl 数据结构CPP文件#include "stdafx.h"#include "squencelist.h"/数据结构部分/sequenlist/sequenlist *InitList()sequenlist*L = (sequenlist*)malloc(sizeof(sequenlist);L->last

28、= 0;return L;/sequenlist*L = new sequenlist;int Length(sequenlist*L)return L->last;int Insert(sequenlist*L, datatype x, int i)int j;if (L->last >= maxsize - 1)cout << "表已满" << endl;return 0;for (j = L->last; j >= i; j-)L->dataj + 1 = L->dataj;L->datai =

29、x;L->last+;return 1;int Delete(sequenlist*L, int i)int j;if (i<1) | (i>L->last)cout << "非法删除位置" << endl;return 0;for (j = i; j <= L->last; j+)L->dataj = L->dataj + 1;L->last-;return 1;int Locate(sequenlist*L, datatype x)int i = 1;while (i <= L->

30、last)if (L->datai != x)i+;else return i;return 0;/*顺序表中删除所有元素为x的结点*/void del_node(sequenlist*L, datatype x)int i = Locate(L, x);while (i != 0)if (!Delete(L, i)break;i = Locate(L, x);void PrintList(sequenlist*L)int i = 1;for (i = 1; i <= L->last; i+)cout << L->datai << ' 'cout << endl;int Compare_L(sequenlist*A, sequenlist*B)int j = 1;int i = 0;int n, m;n = A->last;m = B->last;while (j <= n) && (j <= m)if