【数值分析实验】线性方程组的迭代解法：雅可比迭代、高斯赛德尔迭代、SOR迭代算法（c#）

线性方程组的迭代解法

class Operation
    {
        double[][] a;     //系数矩阵
        double[] b;     //常数向量
        double[] x00,x0, x;     //初始迭代向量和迭代向量
        int n;     //矩阵大小
        public double epsilon = 1e-5;     //最大精度
        int M, m;   //最大迭代向量次数和迭代次数

        double current_e;   //当前最大精度值

        public Operation(int n)    
        {
            this.n = n;
            a = new double[n][];
            for(int i = 0; i < n;i++)
            {
                a[i] = new double[n];
            }
            b = new double[n];
            x0 = new double[n];
            x = new double[n];
            m = 0;
        }     

        public void Init(double[][] a, double[] b,double[] x00, double epsilon = 1e-5, int M = 5000)   //初始化
        {
            this.a = a;
            this.b = b;
            this.epsilon = epsilon;
            this.M = M;
            this.x00 = x00;
            for (int i = 0; i < n; i++)
                x0[i] = x00[i];
        }

        public void Change_x0(double[] x0)     //改变初始向量
        {
            this.x00 = x0;
            for (int i = 0; i < n; i++)
                this.x0[i] = x00[i];
        }

        public void Change_e(double e)     //改变精度
        {
            epsilon = e;
        }

        public void ReSet()     //重置向量
        {
            for (int i = 0; i < n; i++)
                x0[i] = x00[i];
            x = new double[n];
            m = 0;
            current_e = 0;
        }

        public double[] Result()     //返回迭代向量
        {
            return x;
        }

        public int Reslut_m()     //返回迭代次数
        {
            return m;
        }

        public void Show()     
        {
            Console.Write("迭代向量：");
            for (int i = 0; i < 3; i++)
                Console.Write("x" + (i + 1) + "=" + Result()[i] + "  ");
            Console.WriteLine();
            Console.WriteLine("迭代次数：" + Reslut_m());
            Console.WriteLine();
            ReSet();
        }

        public void Jacobi()     //雅克比迭代法
        {
            do
            {
                current_e = 0;
                for(int i = 0;i < n;i++)
                {
                    double sum = 0;
                    for (int j = 0; j < n; j++)
                    {
                        if (j != i)
                        {
                            sum = sum + a[i][j] * x0[j];
                        }
                    }
                    x[i] = (b[i] - sum) / a[i][i];
                }   //更新迭代向量
                m++;   //迭代次数+1
                for (int i = 0; i < n; i++)
                {
                    if (Math.Abs(x[i] - x0[i]) > current_e)
                        current_e = Math.Abs(x[i] - x0[i]);
                }      //计算当前误差	
                for (int i = 0; i < n; i++)
                    x0[i] = x[i];   //更新初始向量
            } while (current_e > epsilon && m < M);  //判断是否仍未达到精度要求且未达到最大迭代次数
        }

        public void Gauss_Seidel()     //高斯-赛德尔迭代法
        {
            do
            {
                current_e = 0;
                for (int i = 0; i < n; i++)
                {
                    double sum = 0;
                    for (int j = 0; j < n; j++)
                    {
                        if (j != i)
                        {
                            if(j < i)
                            {
                                sum = sum + a[i][j] * x[j];
                            }
                            else
                            {
                                sum = sum + a[i][j] * x0[j];
                            }
                        }
                    }
                    x[i] = (b[i] - sum) / a[i][i];
                }   //更新迭代向量
                m++;   //迭代次数+1
                for (int i = 0; i < n; i++)
                {
                    if (Math.Abs(x[i] - x0[i]) > current_e)
                        current_e = Math.Abs(x[i] - x0[i]);
                }      //计算当前误差	
                for (int i = 0; i < n; i++)
                    x0[i] = x[i];   //更新初始向量
            } while (current_e > epsilon && m < M);  //判断是否仍未达到精度要求且未达到最大迭代次数
        }

        public void SOR(double omega)     //SOR迭代算法
        {
            do
            {
                current_e = 0;
                for (int i = 0; i < n; i++)
                {
                    double sum = 0;
                    for (int j = 0; j < n; j++)
                    {
                        if (j != i)
                        {
                            if (j < i)
                            {
                                sum = sum + a[i][j] * x[j];
                            }
                            else
                            {
                                sum = sum + a[i][j] * x0[j];
                            }
                        }
                    }
                    x[i] = (b[i] - sum) / a[i][i];
                    x[i] = omega * x[i] + (1 - omega) * x0[i];
                }   //更新迭代向量
                m++;   //迭代次数+1
                for (int i = 0; i < n; i++)
                {
                    if (Math.Abs(x[i] - x0[i]) > current_e)
                        current_e = Math.Abs(x[i] - x0[i]);
                }      //计算当前误差	
                for (int i = 0; i < n; i++)
                    x0[i] = x[i];   //更新初始向量
            } while (current_e > epsilon && m < M);  //判断是否仍未达到精度要求且未达到最大迭代次数
        }
    }

用法演示

static void Main(string[] args)
        {
            double[][] a = { new double[] { 3, 2, 1 }, new double[] { 0, 5, 1 }, new double[] { 0, 4, 8 } };
            double[] b = { 39, 24, 39 };
            Operation q = new Operation(3);
            q.Init(a, b, new double[] { 1, 1, 1 });

            Console.WriteLine("雅克比迭代法：");
            q.Jacobi();
            q.Show();
            q.ReSet();

            Console.WriteLine("高斯赛德尔迭代法：");
            q.Gauss_Seidel();
            q.Show();
            q.ReSet();
        }