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Some matrix multiplications involving the Hessenberg orthogonality matrix are not currently possible, i.e., the last line in the following code-segment errors:
```
g =complex(randn(2,2))
h = randn(…
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I am aware of PR #904 that will add generic eigenvalue solving to all backends - awesome! Can't wait!
In the meantime, a smaller subset of eigenvalue problems are those where the matrix is upper H…
ibell updated
7 years ago
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There's an infinite number of tricks that could be used here.
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Creating and filling four types of matrices:
- general
- self_adjoint
- triangular, Hessenberg
- banded, diagonal, tridiagonal
For libraries:
- [ ] blaze
- [ ] Eigen
- [ ] Armadillo
- [ ] M…
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- [ ] Stabilised Thomas algorithm. (For tridiagonal solves.)
- [ ] Upper Hessenberg. (Useful inside GMRES? Needs to offer a pseudoinverse solution.)
- [ ] Incremental GMRES
- [ ] Handle "diagonal +…
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It's great that LU / QR / Hessenberg etc was added, but I think SVD would be golden to have as an additional linalg component. A lot of the algorithms from Python bases themself on the SVD decompositi…
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The transformation matrices from the MB03WD periodic Schur decomposition are not computed correctly when the period P increases. The slicot example TMB03WD can be used to reproduce the problem, see at…
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LAPack's Hessenberg eigenvalue routines use half the memory. I'd be willing to make a pull request that moves (and modernizes) ApproxFun.jl's implementation over: https://github.com/JuliaApproximation…
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* Offer iterated classical GS apart from modified GS for better parallel scalability. https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291099-0887%28200001%2916%3A1%3C57%3A%3AAID-CNM320%3E3.0.C…
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The companion matrix is already upper Hessenberg, so it should be possible to use a specialized routine to find its eigenvalues, rather than the general non-symmetric eigenvalue routine. In particula…