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In this question regarding SVD, it is explained why eigen decomposition of $ A^tA $ is not numerically stable compared to "direct SVD algorithms".

Since the former is the algorithm I'm most familiar with, my question is,

out of all algorithms for SVD out there (some of which can be found for example here), which "direct" algorithm would you use if you had to implement numerically stable SVD, using the fixed point arithmetics (say in c++, you only use shorts and can't use floats or doubles)

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Daniel
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  • What do you mean by direct? Are not all the SVD algorithms iterative, unless for matrices of fixed size. – uranix Jun 27 '15 at 10:02
  • @uranix It was a quote from the mentioned question. by "direct" I meant without initially calculating $ A^tA $ – Daniel Jun 27 '15 at 10:22
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    Years of research and experience is required to write an algorithm for computing the SVD. To write an algorithm using shorts is very difficult if not impossible. You have to do a lot of scaling; otherwise there will be accuracy issues and overflow and underflow problems. The standard data type for the SVD is the double. – Vini Mar 12 '17 at 08:40

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