计算

计算方法上机

牛顿迭代

代码

Newton.java

import java.math.BigDecimal;

//注意ep和ws及整数位数有关，这里整数位数为1位
//最后取有效位数 具体参数是小数位数，故取值也与整数位数有关
//迭代时，注意x1要赋值给x0    x0 = x1 ;

public class Newton {
double  approroot ;

double x0;
double x1;
String st1;

int ws ;
double ep ;
public Newton(int ws , double ap) {
this.ws = ws ;
approroot = ap;
x1 = x0 = approroot ;
ep = (1/2)*Math.pow(10, (1 - ws)) ;

}

double f(double  x ){
double x_1;
//        x_1 = (x * x * x -1)/3 ;
x_1 = x - (x * x * x -3 * x -1)/(3*x*x -3) ;
return x_1 ;
}

void calculate(){
int i = 0;
st1 = "x" + i +"  =  " + approroot ;
do {
x0 = x1 ;
i ++ ;
x1 = f(x0);
st1 = st1 + "\n" + "x" + i +"  =  " + x1 ;

} while (Math.abs(x1 - x0) > ep );
st1 = st1 + "\n" + "x" + i +"  =  " + x1 ;
BigDecimal q = new BigDecimal(x1);
x1 = q.setScale(ws - 1, BigDecimal.ROUND_HALF_UP).doubleValue();
}

}

Mainframe.java

import java.awt.Button;
import java.awt.Color;
import java.awt.FlowLayout;
import java.awt.Frame;
import java.awt.TextArea;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;

public class Mainframe extends Frame {

TextArea t1 ,t11;
TextArea t2, t22;
TextArea t3,t33;
TextArea t4,t44;
TextArea t5;
Button button;

public static void main(String[] args) {
new Mainframe().launchframe();

}
void init(){
setLayout(null);

button = new Button("click here to Start");
button.setBounds(500,500,100,50);
button.setForeground(Color.red);
button.setBackground(Color.GREEN);

t1 = new TextArea();
t1.setBounds(210, 50, 200, 50);
t11 = new TextArea();
t11.setText("输入   x : ");
t11.setBounds(10, 50, 200, 50);

t2 = new TextArea();
t2.setBounds(210, 100, 200, 50);
t22 = new TextArea();
t22.setText("输入有效数字位数（阿拉伯数字） : ");
t22.setBounds(10, 100, 200, 50);

t3 = new TextArea();
t3.setBounds(110, 200, 400, 100);
t33 = new TextArea();
t33.setText("中间过程   : ");
t33.setBounds(10, 200, 100, 100);

t4 = new TextArea();
t4.setBounds(110, 300, 400, 50);
t44 = new TextArea();
t44.setText("输出结果 : ");
t44.setBounds(10, 300, 100, 50);

t5 = new TextArea();
t5.setText("方程为：     x * x * x - 3 * x  - 1 = 0");
t5.setBounds(10, 400, 400, 50);
}
public void launchframe() {
init();
setBounds(100, 100, 800, 600);
setBackground(Color.BLUE);
setResizable(false);
add(t1);
add(t2);
add(t3);
add(t4);
add(t11);
add(t22);
add(t33);
add(t44);
add(t5);
add(button);

addWindowListener(new WindowAdapter() {
public void windowClosing(WindowEvent e) {
System.exit(0);
}
});

button.addMouseListener(new MouseAdapter() {
public void mouseClicked(MouseEvent e) {

Newton newton = new Newton(Integer.parseInt(t2.getText()), Double.parseDouble(t1.getText()));

newton.calculate();
t4.setText(newton.x1 + "");
t3.setText(newton.st1);
}
});

setVisible(true);
}

}

setLayout(null); 可设置button位置

二分法（1）

代码

Dichotomy.java

package erfenfa;

public class Dichotomy {

double a, b, ep;

public Dichotomy(double a,double b, double ep) {
this.a = a;
this.b = b;
this.ep = ep;
}

public static void main(String[] args) {
//dic.Calculation();
//        System.out.println(dic.Calculation());

}
double f(double  x ){
double y;
y = x * x * x - 2 * x  - 5 ;
return y ;
}
public  double Calculation(){
double c = b - a;
double a1 = a;
double b1 = b;
for(int i =0 ;c >= ep; i ++){
double middle ;
middle = (a1 + b1) / 2;
if(f(a1)*f(middle) < 0){
b1 = middle ;
c = (b1 - a1)/2 ;   //注意要除2
}
else if (f(a1)*f(middle) > 0) {
a1 = middle;
c = (b1 - a1)/2 ;
}
else {
c = 0;
}

}
return (a1 + b1)/2;
}

}

Mainframe.java

package erfenfa;

import java.awt.Button;
import java.awt.Color;
import java.awt.FlowLayout;
import java.awt.Frame;
import java.awt.TextArea;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;

public class Mainframe extends Frame {

TextArea t1 ,t11;
TextArea t2, t22;
TextArea t3,t33;
TextArea t4,t44;
TextArea t5;
Button button;

public static void main(String[] args) {
new Mainframe().launchframe();

}
void init(){

button = new Button("click here to Start");
button.setForeground(Color.red);
button.setBackground(Color.GREEN);
//        button.setFocusable(true);

t1 = new TextArea();
t1.setBounds(110, 50, 200, 50);
t11 = new TextArea();
t11.setText("Input a ");
t11.setBounds(10, 50, 100, 50);

t2 = new TextArea();
t2.setBounds(110, 100, 200, 50);
t22 = new TextArea();
t22.setText("Input b ");
t22.setBounds(10, 100, 100, 50);

t3 = new TextArea();
t3.setBounds(110, 150, 200, 50);
t33 = new TextArea();
t33.setText("Input ep ");
t33.setBounds(10, 150, 100, 50);

t4 = new TextArea();
t4.setBounds(110, 200, 200, 50);
t44 = new TextArea();
t44.setText("output  ");
t44.setBounds(10, 200, 100, 50);

t5 = new TextArea();
t5.setText("y = x * x * x - 2 * x  - 5 ");
t5.setBounds(10, 300, 300, 50);
}
public void launchframe() {
init();
setBounds(100, 100, 800, 600);
//        setBackground(Color.green);
setResizable(false);
//    setLayout(new FlowLayout(FlowLayout.LEADING, 20 , 40));
add(t1);
add(t2);
add(t3);
add(t4);
add(t11);
add(t22);
add(t33);
add(t44);
add(t5);
add(button);

addWindowListener(new WindowAdapter() {
public void windowClosing(WindowEvent e) {
System.exit(0);
}
});
button.addMouseListener(new MouseAdapter() {
public void mouseClicked(MouseEvent e) {
Dichotomy dic = new Dichotomy(Double.parseDouble(t1.getText()), Double.parseDouble(t2.getText()), Double.parseDouble(t3.getText()));
dic.Calculation();
t4.setText(dic.Calculation() + "");
}
});

setVisible(true);
}

}

二分法（2）

代码

Dichotomy.java

package erfenfa2;

public class Dichotomy {

double a, b, ep , c , result;
double a1 ;
double b1 ;
int time = 0;

public void Dichotomyset(double a,double b) {
this.a = a;
this.b = b;
c = b - a;
a1 = a;
b1 = b;
}

//    public static void main(String[] args) {
//        //dic.Calculation();
////        System.out.println(dic.Calculation());
//
//    }
double f(double  x ){
double y;
y = x * x * x - 2 * x  - 5 ;
return y ;
}

public  void Calculation(){

double middle ;
middle = (a1 + b1) / 2;
if(f(a1)*f(middle) < 0){
b1 = middle ;
c = (b1 - a1) / 2 ;
}
else if (f(a1)*f(middle) > 0) {
a1 = middle;
c = (b1 - a1) / 2 ;
}
else {
c = 0;
}

result =  (a1 + b1)/2;
time ++;
}

}

Mainframe.java
package erfenfa2;

import java.awt.Button;
import java.awt.Color;
import java.awt.FlowLayout;
import java.awt.Frame;
import java.awt.TextArea;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;

public class Mainframe extends Frame {

TextArea t1 ,t11;
TextArea t2, t22;
TextArea t3,t33;
TextArea t4,t44;
TextArea t6,t66;
TextArea t5;
Button button;

boolean first ;
Dichotomy dic;

public static void main(String[] args) {
new Mainframe().launchframe();

}
void init(){
first = true ;
dic = new Dichotomy();

button = new Button("click here to Start");
button.setForeground(Color.red);
button.setBackground(Color.GREEN);

t1 = new TextArea();
t1.setBounds(110, 50, 200, 50);
t11 = new TextArea();
t11.setText("Input a : ");
t11.setBounds(10, 50, 100, 50);

t2 = new TextArea();
t2.setBounds(110, 100, 200, 50);
t22 = new TextArea();
t22.setText("Input b : ");
t22.setBounds(10, 100, 100, 50);

t3 = new TextArea();
t3.setBounds(110, 200, 200, 50);
t33 = new TextArea();
t33.setText("output ep : ");
t33.setBounds(10, 200, 100, 50);

t4 = new TextArea();
t4.setBounds(110, 250, 200, 50);
t44 = new TextArea();
t44.setText("output result : ");
t44.setBounds(10, 250, 100, 50);

t6 = new TextArea();
t6.setBounds(110, 300, 200, 50);
t66 = new TextArea();
t66.setText(" 二分法次数 : ");
t66.setBounds(10, 300, 100, 50);

t5 = new TextArea();
t5.setText("y = x * x * x - 2 * x  - 5 ");
t5.setBounds(10, 400, 300, 50);
}
public void launchframe() {
init();
setBounds(100, 100, 800, 600);
//        setBackground(Color.green);
setResizable(false);
//    setLayout(new FlowLayout(FlowLayout.LEADING, 20 , 40));
add(t1);
add(t2);
add(t3);
add(t4);
add(t11);
add(t22);
add(t33);
add(t44);
add(t5);
add(t6);
add(t66);
add(button);

addWindowListener(new WindowAdapter() {
public void windowClosing(WindowEvent e) {
System.exit(0);
}
});

button.addMouseListener(new MouseAdapter() {
public void mouseClicked(MouseEvent e) {
double aa = Double.parseDouble(t1.getText()) ;
double bb = Double.parseDouble(t2.getText()) ;

if (true == first ) {
dic.Dichotomyset(aa, bb);
first = false ;
}

dic.Calculation();
t4.setText(dic.result + "");
t3.setText(dic.c + "");

t6.setText(dic.time + "");
}
});

setVisible(true);
}

}