Two very basic questions about direct solvers

Hi all,

I have two very basic questions about direct solvers.

1. Why is there convergence problem with direct solvers?
I suppose direct solvers inverse the matrix somehow directly, rather than iteratively, so why is there still convergence problem?

2. How are initial values used for direct solvers?
For iterative solvers I can understand it intuitively, but how does it works for direct solvers?

Best
--
Pu, ZHANG ??
Departamento de Física Teórica de la Materia Condensada,
Universidad Autónoma de Madrid,
Madrid, Spain.