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mathstudy

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[交流] matlab 求解线性方程组Ax=b

x=inv(A)*b;和x=A\b;和迭代法  有什么区别? 前面两个求 A逆 的是基于什么?
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cced_1998

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It takes almost two and one half times as long to compute the solution with y = inv(A)*b as with z = A\b. Both produce computed solutions with about the same error, 1.e-6, reflecting the condition number of the matrix. But the size of the residuals, obtained by plugging the computed solution back into the original equations, differs by several orders of magnitude. The direct solution produces residuals on the order of the machine accuracy, even though the system is badly conditioned.

The behavior of this example is typical. Using A\b instead of inv(A)*b is two to three times as fast and produces residuals on the order of machine accuracy, relative to the magnitude of the data.
11楼2016-03-31 21:37:38
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A=[……],  b=[……],  s=rref([A,b])为佳,如果非满秩,也可知道。
2楼2014-02-07 13:28:11
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戴钢盔的猪头

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如果A不是方阵,它的逆是不存在的。这时inv(A)无法用,但可以用广义逆pinv(A)。而A\b何时都可用。

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3楼2014-02-07 17:09:13
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mathstudy

金虫 (正式写手)


A是可逆方阵, 我想请教的的是  A\b 和 inv(A)*b 中 他们求A逆的 原理 有什么区别, 为什么  A\b比 inv(A)*b 的效率高? 另外  如果是 Gauss 消元法呢?
4楼2014-02-07 19:11:12
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