The main purpose of this paper is to provide a restarting direction for improving on the standard conjugate gradient method.If a drastic non-quadratic behaviour
Let Q be the real quaternion field.Let the set of all matrices A=(α<sub>ij</sub>)<sub>n×m</sub>be Q<sub>n×m</sub>where α<sub>ij</sub>∈Q,A<sup>+</su