数值分析实验之线性方程组的迭代求解(java实现)

 1 package shuzhifenxi;
 2 
 3 
 4 
 5 import java.util.Scanner;
 6 public class J {
 7  static int n = 4;
 8  public static void main(String[] args) {
 9   float[][] A = { { 10, -1, 2,  0 }, { -1, 11, -1,3 },
10     { 2, -1, 10, -1 }, {  0, 3, -1, 8 } };
11   float[] B = { 6, 25, -11, 15 };
12   float e, m, temp, t;
13   float y[] = { 0.0f, 0.0f, 0.0f, 0.0f }, 
14   x0[] = { 0.0f,0.0f, 0.0f, 0.0f },
15   x[] = { 0.0f, 0.0f, 0.0f, 0.0f };
16   int N, i, j, k,sum1,sum2;
17   System.out.println("输入要求的精度e=");
18   Scanner scan = new Scanner(System.in);
19   e = scan.nextFloat();
20   System.out.println("最大迭代次数N=");
21   N = scan.nextInt();
22   for (i = 0; i < n; i++) {
23    System.out.println("x0" + "[" + i + "]=" + x0[i]);
24   }
25   System.out.println("*************************************");
26   System.out.println("以下是Jacobi迭代过程");
27   System.out.println("*************************************");
28   for (k = 0; k < N; k++) {
29    m = 0;
30    for (i = 0; i < n; i++) {
31     x[i] = B[i];
32     for (j = 0; j < n; j++)
33      if (j != i) {
34       x[i] = x[i] - A[i][j] * x0[j];
35      }
36     x[i] = x[i] / A[i][i];
37     System.out.println("x[]" + x[i]);
38     temp = Math.abs(x[i] - x0[i]);
39     System.out.println("temp" + temp);
40     if (temp > m)
41      m = temp;
42    }
43    System.out.print(k + 1 + "次迭代:");
44    
45     
46    for (int i1 = 0; i1 < n; i1++) {
47           System.out.println("x" + "[" + i1 + "]=" + x[i1]);
48     x0[i1] = x[i1];
49    }
50    if (m < e) {
51     sum1=k+1;
52     System.out.println("Jacobi迭代结束");
53     System.out.println("一共迭代了"+sum1+"次");
54     break;
55    }
56    
57   }
58   
59   if (k > N)
60   System.out.println("第" + k + "次迭代未找出满足精度的解 发散");
61   System.out.println("\n");
62   System.out.println("*************************************");
63   System.out.println("以下是Gauss-Seidel迭代");
64   System.out.println("*************************************");
65   for (k = 0; k < N; k++) {
66    m = 0;
67    for (i = 0; i < n; i++) {
68     t=y[i];
69     y[i] = B[i];
70     for (j = 0; j < n; j++)
71      if (j != i) {
72       y[i] = y[i] - A[i][j] * y[j];
73      }
74     y[i] =y[i] / A[i][i];
75     temp = Math.abs(y[i] - t);
76     System.out.println("temp" + temp);
77     if (temp > m)
78      m = temp;
79    }
80    System.out.print(k + 1 + "次迭代:");
81    for (int i1 = 0; i1 < n; i1++) {
82           System.out.println("x" + "[" + i1 + "]=" + y[i1]);
83    }
84    if (m < e) {
85     sum2=k+1;
86     System.out.println("Gauss-Seidel迭代结束");
87     System.out.println("一共迭代了"+sum2+ "次"); 
88     break;
89    }
90    
91    if (k > N)
92     System.out.println("第" + k + "次迭代未找出满足精度的解 发散");
93          
94   }
95   
96      
97      }
98 }