An iterative method of alternating type for systems with special block matrices (Q808616)

The author discusses an iterative method for solving systems of linear algebraic equations of the type \[ \begin{pmatrix} A&D^ T&0 \\ D&B&E^ T \\ 0&E&C \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} f \\ g \\ h \end{pmatrix} \] where A, B and C are symmetric matrices. The proposed algorithm yields a sequence of vectors \(y_ n\) converging to the y-component of the exact solution of (1). The algorithm is illustrated by a numerical example.