A Generalization of the Conjugate-Gradient Method to Solve Complex Systems

The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient metho...

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Bibliographic Details
Published in:IMA journal of numerical analysis 1986-10, Vol.6 (4), p.447-452
Main Author: JACOBS, D. A. H
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Summary:The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient method was developed for symmetric, positive definite systems. In this paper a generalization to complex systems is described by developing the work of Fletcher. The methods improve on ‘symmetrization’, solving the normal equations for the asymmetric case, and expanding the complex system to a real one of twice the order. The method has already proved to be effective.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/6.4.447