Preconditioned conjugate gradient method

The conjugate gradient method is a numerical algorithm that solves a system of linear equations

${\displaystyle Ax=b.\,}$

If the matrix 'A' is ill-conditioned, i.e. it has a large condition number ${\displaystyle \kappa (A)}$, it is often useful to use a preconditioning matrix ${\displaystyle P^{-1}}$ that is chosen such that ${\displaystyle P^{-1}\approx A^{-1}}$ and solve the system

${\displaystyle P^{-1}Ax=P^{-1}b,\,}$

instead.

External links

• Preconditioned Conjugate Gradient – math-linux.com