计算方法(数值分析)实验：解方程组的直接法-追赶法代码实现 java

计算方法(数值分析)实验：解方程组的直接法-追赶法代码实现 java

目的要求：用追赶法求解线性方程组Ax=b，式中A为n阶非奇异方阵，x，b为n阶列向量。要求编写实验程序（语言不限），给出实验结果。

题目1 例5.4

package com.code;

public class main {
    public static void main(String[] args) {
        dao.temo();
    }
}

package com.code;

import java.util.Scanner;

public class dao {
    public static void temo(){

        int n; //矩阵大小
        Scanner s = new Scanner(System.in);
        System.out.print("请输入矩阵的大小：");
        n = s.nextInt();

        int[][] A = new int[n][n], L= new int[n][n], U= new int[n][n];
        int[] f = new int[n], y = new int[n], x = new int[n];

        System.out.println("输入A矩阵的值：");
        for (int i = 0; i < n; i++){
            for(int j = 0; j < n; j ++){
                A[i][j] = s.nextInt();
            }
        }

        System.out.println("输入f矩阵的值：");
        for (int i = 0; i < n; i++) {
            f[i] = s.nextInt();
        }

        for (int i = 0; i < n; i++) { //计算U
            U[i][i] = 1;
        }
        U[0][1] = A[0][1] / A[0][0];
        for (int i = 1; i < n - 1; i++) {
            U[i][i+1] = A[i][i+1] / (A[i][i] - A[i][i-1] * U[i-1][i]);
        }


        L[0][0] = A[0][0];   //计算L
        for (int i = 1; i < n; i++) {
            L[i][i] = A[i][i] - A[i][i-1] * U[i-1][i];
            L[i][i-1] = A[i][i-1];
        }

        y[0] = f[0] / A[0][0];  //计算Y
        for (int i = 1; i < n; i++) {
            y[i] = (f[i] - A[i][i-1] * y[i-1]) / (A[i][i] - A[i][i-1] * U[i-1][i] );
        }

        x[n-1] = y[n-1];  //计算X
        for (int i = n-2; i >= 0; i--) {
            x[i] = y[i] - U[i][i+1] * x[i+1];
        }
        displayTwo(U,n,'U');
        displayTwo(L,n,'L');
        displayOne(y,n,'y');
        displayOne(x,n,'x');
    }

    public static void displayTwo(int arr[][], int n, char c){
        System.out.println("-------------------");
        System.out.println("矩阵" + c + ":");
        for (int[] ints : arr) {
            for (int anInt : ints) {
                System.out.print(anInt + " ");
            }
            System.out.println();
        }
        System.out.println();
    }


    public static void displayOne(int arr[], int n, char c){
        System.out.println("-------------------");
        System.out.println("矩阵" + c + ":");
        for (int i : arr) {
            System.out.print(i + " ");
        }
        System.out.println();
    }
}