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JuliaLinearAlgebra / IterativeSolvers.jl

Iterative algorithms for solving linear systems, eigensystems, and singular value problems
MIT License
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Add LOBPCG docs and bump docs/make.jl Julia version to v0.7 #213

Closed mohamed82008 closed 6 years ago

mohamed82008 commented 6 years ago

Please check if this is correct, I am not sure how to test it.

haampie commented 6 years ago

It also admits a preconditioner and a "constraints" matrix C, such that the algorithm returns the smallest (or largest) eigenvalues associated with the eigenvectors in the nullspace of C'B.

This does not really make sense to me

mohamed82008 commented 6 years ago

The nullspace of A is all vectors x such that Ax = 0. This means that x is orthogonal to all the rows of A. If x is in the nullspace of C'B, then Bx is orthogonal to the rows of C', which are the columns of C. Or in other words, x is B-orthogonal to the columns of C. Long winded but correct :)

haampie commented 6 years ago

Yeah, sure, but the wording is not really what I'd expect in this context. You'd probably want to call it deflation. Also it leaves some questions open: Is C supposed to be B-orthonormal? In that case it really is deflation with (I - CC'B) the projection operator in the standard inner product.