Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming

Authors:
Shao-Liang Zhang;Kazuhide Nakata;Masakazu Kojima
Affiliations:
Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan;Department of Applied Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro, Tokyo 152-0033, Japan
Venue:
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Year:
2002

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Abstract

There is a strong need for the fast solution of large and dense linear systems which arise from the interior-point method for solving Semidefinite Programming with its dual problem. Often direct methods are too expensive in terms of computer memory and CPU-time requirements, then the only alternative is to use iterative methods. Here, a class of incomplete orthogonalization preconditioners for the conjugate gradient method for solving this type of linear systems will be proposed. The efficient feature of the preconditioners will be confirmed by several numerical experiments.