Matrix preconditioning
= Matrix preconditioning
{title2=$M^{-1/2}AM^{-1/2}$}
Matrix preconditioning transforms a system using an inexpensive auxiliary solve to improve its spectrum. For symmetric positive definite matrices, a positive definite $M$ produces $M^{-1/2}AM^{-1/2}$, preserving the symmetric structure needed by <Conjugate gradient method>.