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I'm interested what fdej thinks about this one. arb has recently been merged with flint under his maintainership and is getting some generic rings wrapper and m
by ftxbro 4y ago
I'm interested what fdej thinks about this one. arb has recently been merged with flint under his maintainership and is getting some generic rings wrapper and more interfaces with other languages. But maybe its focus is more like algebraic things like modular forms and less like tensor libraries for machine learning and GPGPU.
https://news.ycombinator.com/user?id=fdej https://news.ycombinator.com/user?id=fdej
https://news.ycombinator.com/item?id=26054520 https://news.ycombinator.com/item?id=26054520
https://arblib.org/ https://arblib.org/
- fdej 4y agoThis looks quite similar like the "Lagrange models" defined by Joris van der Hoeven in https://hal.science/hal-01188378/document https://hal.science/hal-01188378/document, a version of Taylor models where the constant error term is replaced by an interval multiple of x^n. Representing functions locally is a very interesting problem: there are lots of possible approaches using intervals, Taylor series, Chebyshev series, etc. Big open design space if you ask me.
- ogogmad 4y agoSee my comment above about your linear algebra implementation.
- ogogmad 4y agoI've just looked at the documentation for eigenvalues and eigenvectors in arblib. I was thinking that: - Eigenvectors are not computable in regions surrounding eigenvalue clashes. Therefore you should never compute them. - Let M be a symmetric matrix being eigen-decomposed. The decomposition should be A = P D P^(-1) where only D is interval-valued, and P and P^(-1) are NOT UNDER ANY CIRCUMSTANCE INTERVAL-VALUED, and A should include M.
- ftxbro 4y agoI see what you mean, but say you have such a matrix and there are two eigenvalues that you can't separate from each other. Then wouldn't their corresponding eigenvectors define like a 2d plane? Couldn't there still be some interval for that plane, like say that the plane is defined by the linear combination of two vectors and both vectors have zero on some coordinate, say the x coordinate. The interval could still be helpful by saying that any combination will also be zero there, right?