Cholesky Decomposition of a Sparse Symmetric Positive Semidefinite (SPSD) Singular Matrix

Specific Domains Numerics
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I see.
Summarizing the case of solving a linear system with rank deficient SPSD matrix:

  1. Dense Case: Use the Bunch Kaufman decomposition (Sometimes called LDLt as well, see Shouldn’t bunchkaufman() Be Named ldlt()).
  2. Sparse Case: Use the LDLt decomposition.

In case \boldsymbol{b} \in R \left( \boldsymbol{A} \right), one may use Cholesky Decomposition with check = false. Yet the decomposition is not guaranteed to work still.