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SciML / ExponentialUtilities.jl

Fast and differentiable implementations of matrix exponentials, Krylov exponential matrix-vector multiplications ("expmv"), KIOPS, ExpoKit functions, and more. All your exponential needs in SciML form.

Home Page:https://docs.sciml.ai/ExponentialUtilities/stable/

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Output-sensitive Lanczos iteration

mforets opened this issue · comments

commented

In [Algorithm 4, 1] the authors describe an "output-sensitive" Lanczos iteration scheme in the sense that the user can specify a projection matrix that's applied inside the iteration. To my non-expert understanding such option is not available in this library. In any case I'd be interested in contributing but some guidance would be very helpful.

We've used arnoldi!(Ks, Aᵀ, ℓ; m=m, ishermitian=hermitian, tol=tol) and cited ExponentialUtilities.jl in an upcoming paper. Being able to specify a projection matrix would give a huge boost in performance for large problems.

cc @jorgepz

[1] Bak, S., Tran, H. D., & Johnson, T. T. (2019, April). Numerical verification of affine systems with up to a billion dimensions. In Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control (pp. 23-32).
https://arxiv.org/abs/1804.01583

commented

It's not available yet, but it shouldn't be too hard? @YingboMa can probably comment.