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docs: remove outdated section
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docs/src/index.md

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@@ -403,24 +403,3 @@ An overview of what we have, how it's done and what we're missing.
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simply computing the matrix-matrix product `V := V * Q`, where `V` is the
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original orthonormal basis. This is not in-place in `V`, so we allocate a bit
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of scratch space ahead of time.
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### Not implemented
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- Being able to kickstart the method from a given Arnoldi relation. This also
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captures:
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1. Making an initial guess by providing a known approximate eigenvector;
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2. Deflating some subspace by starting the Arnoldi method with a given partial
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Schur decomposition.
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- Matrix-induced inner product for generalized eigenvalue problems.
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- Efficient implementation of symmetric problems with Lanczos.
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On my wish list is to allow custom vector or matrix types, so that we can
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delegate expensive but trivial work to hardware that can do it faster
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(distributed memory / GPU). The basic concept would be:
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1. The core Arnoldi method performs tedious linear algebra on the projected,
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low-dimensional problem, but finally just outputs a change of basis in the
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form of a unitary matrix Q.
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2. Appropriate hardware does the change of basis `V := V * Q`.
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Similar things should happen for expansion of the subspace and
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orthogonalization.

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