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Given $ w,x,y \in \mathbf{R^{n}}$

which one has better numerical properties?

(1) $ w = z - (x \cdot y^{T}) \cdot z$

(2) $ w = z - x \cdot (y^{T} \cdot z)$

First one needs more FLOPS (thus more possible floating point arithmetic errors) and storage to be solved. Which is more robust to perturbations?

tomtom
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    If you set aside floating point issues, then they're going to be exactly the same in terms of sensitivity to mathematical perturbations. – Ian Nov 09 '17 at 19:54

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