October 23, 2017

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Singular Value Decomposition for Programmers

There’s a very important way in which SVD can help us with Linear Systems.

We start from (Ax=b), and then have (x = A^{-1}b=(U Sigma V^T)^{-1}b=sum_{i=1}^n{dfrac{u_i^t b}{sigma_i}})

Now, if (sigma_i) is small enough, small change in (A) or (b) will cause large changes in (X), andthe system becomes unstable.

News Source : Singular Value Decomposition for Programmers

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