8. Methods Related to the Normal Equations

There are a number of techniques for converting a nonsymmetric linear system into a symmetric one. One such technique solves the equivalent linear system ATAx = ATb, called the normal equations. Often, this approach is avoided in practice because the coefficient matrix ATA is much worse conditioned than A. However, the normal equations approach may be adequate in some situations. Indeed, there are even applications in which it is preferred to the usual Krylov subspace techniques. This chapter covers iterative methods that are either directly or implicitly related to the normal equations.