Preconditioning

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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.


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