Assuming that a LU decomposition exists for all desired submatrices of a matrix
a, is there an easy way to extract the decomposition for the submatrix from the decomposition of
a? It is easy in this example:
julia> using LinearAlgebra julia> a = randn(10,10); julia> a2 = a[1:5,1:5]; julia> P = lu(a, NoPivot()); julia> P2 = lu(a2, NoPivot()); julia> P.factors[1:5,1:5] ≈ P2.factors true
In that way I can compute the decomposition of the large matrix
a once and then simply view the decomposition for each desired submatrix.
My question is: Can I do the same when I do not want the submatrix with indices
1:n, but arbitrary subindices. It would be good also, I guess, if
NoPivot() is not a requirement. And most importantly: can I do this for the UMFPACK LU for sparse matrices?
Thank you for any help.