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Comment by fdej | Hacker News Reader

What makes you say that? I've had good speedups with Strassen multiplication in variable precision (or with floating-point, in case you meant fixed-point arithmetic).

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Strassen method is faster than native multiplication, but it is not stable: you will get much larger rounding errors when implementing it using floating point numbers, compared to native multipllication. And fine precision is required for a lot of algorithm implemented using matrix multiplication, such as matrix inversion or gradient descent, so this is often a problem.

do we know if the rounding errors are a big deal for numerical methods that can tolerate inaccuracy (like gradient descent for machine learning)?

You want to converge on a local minimum, don't you? We can't guarantee that with unstable algorithms.

Rounding errors, underflows and instability in floats are very well known problems, a big deal if you do anything but graphics.

It depends. I have seen some algorithms (the example that comes to mind was a clustering) become worse solely due to numerical error.

When that happens, if you are not equiped to measure the numerical error or at least trained to suspect it, you might think that it is just the algorithm that is not working.

Speed is fine. The issue is numerical stability.

Yes, indeed, and Strassen is a bad default algorithm because of this. There are specialized situations where the numerical stability isn't an issue though.

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