Question

我将这个方程系统设为一组1 ≤ n ≤ 30

−(2 + α)x1 + x2 = b1,
xj−1 − (2 + α)xj + xj+1 = bj , for 2 ≤ j ≤ 29,
x29 − (2 + α)x30 = b30.

α= 1 我们假设膜保持在端点（即x0 = 0和x31 = 0）。膜上没有重量，因此对于j = 1，所有bj = 0。。。 30除了j = 6，其中施加负荷：b6 = 2。

我想计算系统的LU分解。我不知道如何在matlab中实现系统的左侧。右边我这样做了：

b=[0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]';

如何做左侧？

由于

Answer 1

It's unclear why you have included the entire linear system if you are only interested in the LU factorization of A? Regardless, here is some code which generates your A matrix as described above, and solves the linear system and shows the LU factorization.

% equation A*X = b

b = zeros(30,1);
b(6) = 2;
alpha = 1;

A = zeros(30, 30);

A(1, 1) = -(2 + alpha);
A(1, 2) = 1;

for i = 2:29
    A(i, i-1) = 1;
    A(i, i) = -(2 + alpha);
    A(i, i+1) = 1;
end

A(30, 29) =  1;
A(30, 30) = -(2 + alpha);

You can then get the LU factorization using lu(A) or solve the linear system of equations using linsolve(A,b).

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