帮我用c++写一个landweber迭代算法

好的，我可以回答这个问题。以下是一个简单的 Landweber 迭代算法的 C 代码示例：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define MAX_ITERATIONS 100
#define TOLERANCE 1e-6

void landweber(double *x, double *b, double **A, int n, double alpha) {
    int i, j, k;
    double *Ax, *r, *x_new, norm_r, norm_b;

    Ax = (double *) malloc(n * sizeof(double));
    r = (double *) malloc(n * sizeof(double));
    x_new = (double *) malloc(n * sizeof(double));

    for (k = ; k < MAX_ITERATIONS; k++) {
        // Compute A*x
        for (i = ; i < n; i++) {
            Ax[i] = .;
            for (j = ; j < n; j++) {
                Ax[i] += A[i][j] * x[j];
            }
        }

        // Compute residual r = b - A*x
        for (i = ; i < n; i++) {
            r[i] = b[i] - Ax[i];
        }

        // Compute norm of residual
        norm_r = .;
        for (i = ; i < n; i++) {
            norm_r += r[i] * r[i];
        }
        norm_r = sqrt(norm_r);

        // Compute norm of b
        norm_b = .;
        for (i = ; i < n; i++) {
            norm_b += b[i] * b[i];
        }
        norm_b = sqrt(norm_b);

        // Check for convergence
        if (norm_r / norm_b < TOLERANCE) {
            break;
        }

        // Update x
        for (i = ; i < n; i++) {
            x_new[i] = x[i] + alpha * A[i][i] * r[i];
        }
        for (i = ; i < n; i++) {
            x[i] = x_new[i];
        }
    }

    free(Ax);
    free(r);
    free(x_new);
}

int main() {
    int i, j, n;
    double alpha;
    double *x, *b, **A;

    // Read input data
    scanf("%d %lf", &n, &alpha);

    x = (double *) malloc(n * sizeof(double));
    b = (double *) malloc(n * sizeof(double));
    A = (double **) malloc(n * sizeof(double *));
    for (i = ; i < n; i++) {
        A[i] = (double *) malloc(n * sizeof(double));
        for (j = ; j < n; j++) {
            scanf("%lf", &A[i][j]);
        }
    }
    for (i = ; i < n; i++) {
        scanf("%lf", &b[i]);
    }

    // Run Landweber algorithm
    landweber(x, b, A, n, alpha);

    // Print solution
    for (i = ; i < n; i++) {
        printf("%lf ", x[i]);
    }
    printf("\n");

    // Free memory
    free(x);
    free(b);
    for (i = ; i < n; i++) {
        free(A[i]);
    }
    free(A);

    return ;
}

这个程序读入一个 n x n 的矩阵 A，一个 n 维向量 b，以及一个参数 alpha，然后运行 Landweber 迭代算法来求解线性方程组 Ax = b。算法的终止条件是残差的范数小于一个给定的容差 TOLERANCE 或者达到最大迭代次数 MAX_ITERATIONS。