算法步骤

  1. 输入矩阵A，常数项b，初始迭代向量x1，迭代后向量x2，容许误差error
  2. x(i)=(b(i)-∑(a(i,j)*x(j)))/a(i,i) j!=i1
  3. 若x2-x1的每一项都小于error，则输出x2，结束程序；否则转步骤2
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% assignment4.m

function [x2] = assignment4(A,b,x1,error)
%  inputs:
%         A:系数矩阵，维度为n*n
%         b:载荷矩阵，维度为n*1
%         error:容许误差
%  outputs:
%         x2:迭代后矩阵，维度n*1
%         x1:迭代前矩阵，维度n*1

[A_row,A_col] = size(A);
e=1;
x2=x1;

while e>error
    for i1=1:A_row
        x2(i1)=b(i1);
        for i2=1:A_col
            if i1~=i2
                x2(i1)=x2(i1)-x2(i2)*A(i1,i2);
            end
        end
        x2(i1)=x2(i1)/A(i1,i1);
    end
    
    e=x2(1)-x1(1);
    for i1=2:A_row
        if x2(i1)-x1(i1)>e
            e=x2(i1)-x1(i1);
        end
    end
    x1=x2;
end
end

% 命令行输入
% assignment4([10 -1 -2; -1 10 -2; -1 -1 5],[7.2 8.3 4.2],[0 0 0],0.0001)
% assignment4([10 -1 -2; -1 10 -2; -1 -1 5],[7.2 8.3 4.2],[1 1 1],0.0001)