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A General Approach to the Formulae Used in the Conjugate Directions Method for Solving Linear Systems of Algebraic Equations

A proof of the formulae used in the conjugate directions method for solving linear algebraic systems of equations is presented. The proof is based on the minimization of a functional connected with a change of variables, and differs from the proofs presented by other authors. It permits an accessible but deep understanding of the procedure removing some confusions of literature, and allowing new remarks. Some results may be easily verified by using Maplesoft programs.