Implementation of saddle-point minimal residual solvers

Abstract

In this thesis, we describe the implementation of the Saddle-Point Minimal Residual (SPMR) solvers developed by Estrin and Greif. These solvers compose a family of iterative methods for the solution of large and sparse saddle-point systems: linear systems of the form $$ \begin{bmatrix} A & G_1^T \\ G_2 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} f \\ g \end{bmatrix}, $$ where $A \in \mathbb{R}^{n \times n}$, $G_1, G_2 \in \mathbb{R}^{m \times n}$, $f \in \mathbb{R}^{n}$, and $g \in \mathbb{R}^{m}$ (with $n > m$).