Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
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TL;DR
A (modified) minimal residual (least square) method is presented, which converges for systems with matrices that have a positive definite symmetric part and preconditioning and rate of convergence are discussed.
Abstract
Conjugate gradient type methods are discussed for unsymmetric and inconsistent system of equations. For unsymmetric problems, besides conjugate gradient methods based on the normal equations, we also present a (modified) minimal residual (least square) method, which converges for systems with matrices that have a positive definite symmetric part. For inconsistent problems, for completeness we discuss briefly various (well-known) versions of the conjugate gradient method. Preconditioning and rate of convergence are also discussed.