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If you look up numerical algorithm in Wikiepedia you will find plenty of discussion of error bounds. Of course matrix multiplication performed on exact numbers
by Analog24 4y ago
If you look up numerical algorithm in Wikiepedia you will find plenty of discussion of error bounds. Of course matrix multiplication performed on exact numbers doesn't have errors, the calculation is exact. Computers and the algorithms they run do not have that luxury when dealing with approximations.
- DannyBee 4y agoOf course you will, because those are about how they are implemented on computers with limited precision. Your point is exactly mine - correctness is usually defined on exact numbers, which does not have error bounds. Usefulness is defined by particular implementation choices and precision choices when implemented on a particular computer. The entire argument here is (crazily) that you can't prove correctness without error bounds, correctness is always context specifi. Of course you can, and of course it's not. Just like the wikipedia algorithm shows. That may or may not make it useful for a particular application.