nLab
preconditioner

Contents

Idea

A preconditioner (matrix) is a matrix which multiplies (from left or from right, thus left and right preconditioners) the matrix of coefficients of a system which discretizes a differential equation in order to get faster convergence (=smaller condition number) of iterative numerical solution techniques. As a technique, preconditioning is used also for optimization algorithms.

Literature

  • wikipedia preconditioner
  • Owe Axelsson, Iterative Solution Methods, Cambridge University Press 1996
  • J. H. Bramble, J.E. Pasciak, A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems, Math. Comp. 50 (1988) 1–17
  • Tyrone Rees, Martin Stoll, Andy Wathen, All-at-once preconditioning in PDE-constrained optimization, Kybernetika 46:2 (2010) 341 – 360 pdf
  • John W. Pearson, Martin Stoll, Andy Wathen, Regularization-robust preconditioners for time-dependent PDE constrained optimization problems, SIAM J. Matrix Anal. and Appl., 33(4), 1126–1152, 2012 doi
  • Michele Benzi, Preconditioning techniques for large linear systems: a survey, J. of Computational Physics 182, 418–477 (2002) doi pdf
category: applications

Last revised on December 5, 2013 at 09:18:49. See the history of this page for a list of all contributions to it.