# Preconditioning

A generalization of scaling that modifies the hessian so as to improve convergence properties. In the case of quadratic programming, this typically means multiplying the quadratic form matrix, $LaTeX: Q,$ by a preconditioner, $LaTeX: P,$ so that the condition number of $LaTeX: PQ$ is as close to 1 as possible. There are many variations, including splitting a matrix, $LaTeX: Q = P - S,$ to achieve a better conditioned matrix in the sense of its eigenvalue (and eigenspace) structure that governs convergence properties of algorithms like steepest ascent and conjugate gradient.