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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 n
by SuchAnonMuchWow 5y ago
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.
- dnautics 5y agodo we know if the rounding errors are a big deal for numerical methods that can tolerate inaccuracy (like gradient descent for machine learning)?
- klyrs 5y agoYou want to converge on a local minimum, don't you? We can't guarantee that with unstable algorithms.
- hamilyon2 5y agoRounding errors, underflows and instability in floats are very well known problems, a big deal if you do anything but graphics.
- nestorD 5y agoIt 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.