CGNE - preconditioned conjugate gradient method applied to the normal equations without explicitly forming AtA.
Usage:
-ksp_type cgne
Options:
-ksp_cg_type
indicates the complex matrix is Hermitian or symmetric
(one of)
Hermitian
symmetric
Notes: eigenvalue computation routines will return information about the spectrum of AtA, rather than A.Drawbacks: Convergence is very slow for CFD problems since the condition number of AtA is the square of the condition number of A.These methods are based on the application of the CG method to one of two forms of the normal equations for . CGNE solves the system for and then computes the solution . CGNR solves for the solution vector where . When the coefficient matrix is nonsymmetric and nonsingular, the normal equations matrices and will be symmetric and positive definite, and hence CG can be applied. The convergence may be slow, since the spectrum of the normal equations matrices will be less favorable than the spectrum of .