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 > <[email protected]> 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
