Sparse Linear Algebra

Sparse matrix solvers call functions from SuiteSparse. The following factorizations are available:

SuiteSparse.CHOLMOD.FactorCholesky factorization
SuiteSparse.UMFPACK.UmfpackLULU factorization
SuiteSparse.SPQR.QRSparseQR factorization

Other solvers such as Pardiso.jl are as external packages. Arpack.jl provides eigs and svds for iterative solution of eigensystems and singular value decompositions.

These factorizations are described in the Linear Algebra section of the manual:

  1. cholesky
  2. ldlt
  3. lu
  4. qr
lowrankupdowndate!(F::CHOLMOD.Factor, C::Sparse, update::Cint)

Update an LDLt or LLt Factorization F of A to a factorization of A ± C*C'.

If sparsity preserving factorization is used, i.e. L*L' == P*A*P' then the new factor will be L*L' == P*A*P' + C'*C

update: Cint(1) for A + CC', Cint(0) for A - CC'