連立一次方程式を解く

ガウス・ザイデル法という解き方。
だんだん解が収束していきます。

  4w +1x +2y= 21
  2w +5x -1y= 14
  1w +3x -7y=-24
w(0)= 5.3 x(0)= 0.7 y(0)= 4.5 
w(1)= 2.8 x(1)= 2.6 y(1)= 4.9 
w(2)= 2.1 x(2)= 2.9 y(2)= 5.0 
w(3)= 2.0 x(3)= 3.0 y(3)= 5.0 
w(4)= 2.0 x(4)= 3.0 y(4)= 5.0 
w(5)= 2.0 x(5)= 3.0 y(5)= 5.0 
w(6)= 2.0 x(6)= 3.0 y(6)= 5.0 
w(7)= 2.0 x(7)= 3.0 y(7)= 5.0 
w(8)= 2.0 x(8)= 3.0 y(8)= 5.0 
w(9)= 2.0 x(9)= 3.0 y(9)= 5.0 
w= 2 x= 3 y= 5 

public class LinearSystem {
    public static void main(String[] args){
        //右辺の係数
        a = new double[][]{
            {4, 1, 2},
            {2, 5, -1},
            {1, 3, -7}
        };
        //左辺値
        y = new double[]{
            21, 14, -24
        };
        //求める値
        x = new double[]{
            2, 3, 5
        };
        //式の表示
        String[] ch = {"x", "y", "z"};
        for(int i = 0; i < a.length; ++i){
            String str = "";
            for(int j = 0; j < a[i].length; ++j){
                str += String.format(" %" + 
                        ((j == 0) ? " " : "+") +
                        "2.0f%s", a[i][j], ch[j]);
            }
            System.out.printf("%s=% 2.0f%n", str, y[i]);
        }
        //解を計算する
        double[] s = new double[x.length];
        for(int n = 0; n < 10; ++n){//とりあえず10回
            for(int i = 0; i < x.length; ++i){
                double sum = 0;
                for(int j = 0; j < x.length; ++j){
                    if(i == j) continue;
                    sum += a[i][j] * s[j];
                }
                s[i] = (y[i] - sum) / a[i][i];
            }
            for(int j = 0; j < x.length; ++j){
                System.out.printf("%s(%d)=% 2.1f ", ch[j], n, s[j]);
            }
            System.out.println();
        }
        //準備していた解の表示
        for(int i = 0; i < x.length; ++i){
            System.out.printf("%s=% 2.0f ", ch[i], x[i]);
        }
        System.out.println();
    }
}