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lines changed Original file line number Diff line number Diff line change @@ -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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-
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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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-
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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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-
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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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-
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- Similar things should happen for expansion of the subspace and
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- orthogonalization.
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