### 43.1 Overview

This chapter is primarily concerned with the solution of the linear system

    A x = b

where A is a general square n-by-n non-singular sparse matrix, x is an unknown n-by-1 vector, and b is a given n-by-1 right hand side vector. There exist many methods for solving such sparse linear systems, which broadly fall into either direct or iterative categories. Direct methods include LU and QR decompositions, while iterative methods start with an initial guess for the vector x and update the guess through iteration until convergence. GSL does not currently provide any direct sparse solvers.