[petsc-users] Spectrum slicing, Cholesky factorization for positive semidefinite matrices

[Jose E. Roman]

The spectrum slicing method computes the Cholesky factorization of (A-sigma*B) or (A-sigma*I) for several values of sigma. This matrix is indefinite, it does not matter if your B matrix is semi-definite. If B is singular, the only precaution is that you have to use purification, but this option is turned on by default so no problem.

Jose


> El 10 feb 2020, a las 14:32, Jan Grießer via petsc-users <petsc-users at mcs.anl.gov> escribió:
> 
> Hello, everybody,
> i want to use the spectrum slicing method in Slepc4py to compute a subset of the eigenvalues and associated eigenvectors of my matrix. To do this I need a factorization that provids the Matrix Inertia. The Cholesky decomposition is given as an example in the user manual. The problem ist that my matrix is not positive definit but positive semidefinit (Three eigenvalues are zero). The PETSc user forum only states that for the Cholesky factorization a symmetric matrix is zero, but as far is i remember the Chosleky factorization is only numerical stable for positive definite matrices. Can i use an LU factorization for the spectrum slicing, although the PETSc user manual states that the Inertia is accessible when using Cholseky? Or can is still use Chollesky? 
> Greetings Jan