Gauss-Seidel解线性方程组

import java.util.Scanner;public class Gauss_Seidel {/** * @param args */public static void main(String[] args) {Scanner scan = new Scanner(System.in);double error = 0.00001;//结果的误差许可范围System.out.println("请输入线性方程的元数：");int n = scan.nextInt();double x1[] = new double[n+1];//数组去掉0值，与矩阵保持统一。x分量要双倍存储，存放新的和上一步的变量 double x2[] = new double[n+1];double a[][] = new double[n+1][n+1];//系数矩阵double b[] = new double[n+1];//AX=B中的矩阵BSystem.out.println("请输入系数矩阵");for(int i = 1 ; i <= n; i++){for(int j = 1 ; j <= n ; j++){a[i][j] = scan.nextDouble();}}System.out.println("请输入矩阵B：");for(int i = 1 ; i <= n ; i++){b[i] = scan.nextDouble();}System.out.println("请输入解的初始估计值：");for(int i = 1 ; i <= n ; i++){x1[i] = scan.nextDouble();}for(int i = 1 ; i <= n ; i++)x2[i] = x1[i];boolean done = true;//最后求解的值是否在误差许可范围内boolean x1_new = false;//用于判断x1和x2哪个存放新的结果boolean x2_new = true;int count = 1;//记录Gauss_seidel运算次数while(done){for(int i = 1 ; i <= n ; i++){double m = 0;//暂存中间结果for(int j = 1 ; j <= n ;j++){if(j!=i){if(x2_new){//新结果存于x2中if(i>j)m += a[i][j]*x2[j];//塞德尔方法可以用求的新的值代入、elsem += a[i][j]*x1[j];}else{//新结果要存于x1中if(i>j)m += a[i][j]*x1[j];elsem += a[i][j]*x2[j];}}}if(x2_new) {x2[i] = (b[i]-m)/a[i][i];}else{x1[i] = (b[i]-m)/a[i][i];}}if(x2_new) {x2_new = false;x1_new = true;//x1下次将存放新的结果}else{x1_new = false;x2_new = true;}for(int i = 1 ; i <= n;i++){if(Math.abs(x1[i]-x2[i]) > error){//绝对值大于误差允许范围则继续迭代done = true;break;}elsedone = false;}System.out.println(count+"次Gauss_Seidel运算后的结果为： ");for(int i = 1 ; i <= n ; i++){if(x1_new)System.out.println("x"+i+" = "+x2[i]);elseSystem.out.println("x"+i+" = "+x1[i]);}count++;}System.out.println("线性方程组的解为：");for(int i = 1 ; i <= n ; i++){if(x1_new)System.out.println("x["+i+"] = "+x2[i]);elseSystem.out.println("x["+i+"] = "+x1[i]);}}}