Semi-Conjugate Direction Methods for Nonsymmetric Systems
نویسندگان
چکیده
In this preliminary work, left and right conjugate vectors are deened for nonsymmetric, nonsin-gular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving nonsymmetric systems of linear equations is proposed. The method reduces to the usual conjugate gradient method when A is symmetric positive deenite. A nite termination property of the semi-conjugate direction method is shown, providing a new simple proof of the-nite termination property of conjugate gradient methods. The new method is well deened for all nonsingular M-matrices. Some techniques for overcoming breakdown are suggested for general non-symmetric A. The connection between the semi-conjugate direction method and LU decomposition is established. The semi-conjugate direction method is successfully applied to solve some sample linear 1 systems arising from linear partial diierential equations, with attractive convergence rates. Further analysis and experiments are needed.
منابع مشابه
Semi-Conjugate Direction Methods for Real Positive Definite Systems∗
In this preliminary work, left and right conjugate direction vectors are defined for nonsymmetric, nonsingular matrices A and some properties of these vectors are studied. A left conjugate direction (LCD) method for solving general systems of ∗The work of the first author was partially supported by CNPq, CAPES, Fundação Araucária, Brazil. The work of the second author was partially supported by...
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