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Dual numbers are magic. They are somewhat obscure but very powerful e.g for reasoning about dynamically evolving systems. They are like complex numbers but inst
by adamnemecek 8y ago
Dual numbers are magic. They are somewhat obscure but very powerful e.g for reasoning about dynamically evolving systems. They are like complex numbers but instead of i^2=-1 you have epsilon such that epsilon^=0. Shit gets real from then on.
Dual number functions give you the value at the function as well as the derivative at that point. Very cool.
- nestorD 8y agoAnd if you want the second derivative... You have hyper-dual numbers! http://adl.stanford.edu/hyperdual/ http://adl.stanford.edu/hyperdual/
- eigenspace 8y agoThat’s not normally necessary. One can often just use tagged dual numbers. I guess one might consider tagged duals hyperduals.
- adamnemecek 8y agoWhat’s a tagged number? Google isn’t helpful.
- banach 8y agoWhy settle for two, when you can have them all? https://link.springer.com/article/10.1023/A:1011501232197 https://link.springer.com/article/10.1023/A:1011501232197