## A New Conjugate Gradient Algorithm Incorporating Adaptive Ellipsoid Preconditioning

The conjugate gradient (CG) algorithm is well-known to have excellent theoretical properties for solving linear systems of equations $Ax = b$ where the $n\times n$ matrix $A$ is symmetric positive definite. However, for extremely ill-conditioned matrices the CG algorithm performs poorly in practice. In this paper, we discuss an adaptive preconditioning procedure which improves the … Read more