  A simple alternative to the conjugate gradient(CG) method is presented; this
method is developed as a special case of the more general iterated Ritz method
(IRM) for solving a system of linear equations. This novel algorithm is not
based on conjugacy, i.e. it is not necessary to maintain overall
orthogonalities between various vectors from distant steps. This method is more
stable than CG, and restarting techniques are not required. As in CG, only one
matrix-vector multiplication is required per step with appropriate
transformations. The algorithm is easily explained by energy considerations
without appealing to the A-orthogonality in n-dimensional space. Finally,
relaxation factor and preconditioning-like techniques can be adopted easily.
